There were 1,300 direct flights to 17 cities before President Trump’s travel restrictions. Since then, nearly 40,000 Americans and other authorized travelers have made the trip, some this past week and many with spotty screening.

Since Chinese officials the outbreak of a mysterious pneumonialike illness to international health officials on New Year’s Eve, at least 430,000 people have arrived in the United States on direct flights from China, including nearly 40,000 in the two months after President Trump imposed restrictions on such travel, according to an analysis of data collected in both countries.

The bulk of the passengers, who were of multiple nationalities, arrived in January, at airports in Los Angeles, San Francisco, New York, Chicago, Seattle, Newark and Detroit. Thousands of them flew directly from Wuhan, the center of the coronavirus outbreak, as American public health officials were only beginning to assess the risks to the United States.

Flights continued this past week, the data show, with passengers traveling from Beijing to Los Angeles, San Francisco and New York,  from the clampdown that took effect on Feb. 2. In all, 279 flights from China have arrived in the United States since then, and screening procedures have been uneven, interviews show.

Mr. Trump has repeatedly suggested that his travel measures impeded the virus’s spread in the United States. “I do think we were very early, but I also think that we were very smart, because we stopped China,” he said at a briefing on Tuesday, adding, “That was probably the biggest decision we made so far.” Last month, he said, “We’re the ones that kept China out of here.”

But the analysis of the flight and other data by The New York Times shows the travel measures, however effective, may have come too late to have “kept China out,” particularly in light of  that as many as 25 percent of people infected with the virus may never show symptoms. Many infectious-disease experts suspect that the virus had been spreading undetected for weeks after the first American case was confirmed and that it had continued to be introduced. In fact, no one knows when the virus first arrived in the United States.

During the first half of January no travelers from China were screened for potential exposure to the virus. Health screening began in mid-January, but only for a number of travelers who had been in Wuhan and only at the airports in Los Angeles, San Francisco and New York. By that time, about 4,000 people had already entered the United States directly from Wuhan, according to VariFlight, an aviation data company based in China. The measures were expanded to all passengers from China two weeks later.

In a statement on Friday, Hogan Gidley, a White House spokesman, described Mr. Trump’s travel restrictions as a “bold decisive action which medical professionals say will prove to have saved countless lives.” The policy took effect, he said, at a time when the global health community did not yet “know the level of transmission or asymptomatic spread.”

Trump administration officials have also said they received significant pushback about imposing the restrictions even when they did.

In interviews, multiple travelers who arrived after the screening was expanded said they received only passing scrutiny, with minimal follow-up.

“I was surprised at how lax the whole process was,” said Andrew Wu, 31, who landed at Los Angeles International Airport on a flight from Beijing on March 10. “The guy I spoke to read down a list of questions, and he didn’t seem interested in checking out anything.”

Sabrina Fitch, 23, flew from China to Kennedy International Airport in New York on March 23. She and the 40 or so other passengers had their temperature taken twice while en route and were required to fill out forms about their travels and health, she said.

“Besides looking at our passports, they didn’t question us like we normally are questioned,” said Ms. Fitch, who had been teaching English in China. “So it was kind of weird, because everyone expected the opposite, where you get a lot of questions. But once we filled out the little health form, no one really cared.”

In January, before the broad screening was in place, there were over 1,300 direct passenger flights from China to the United States, according to VariFlight and two American firms, MyRadar and FlightAware. About 381,000 travelers flew directly from China to the United States that month, about a quarter of whom were American, according to data from the Department of Commerce’s International Trade Administration.

In addition, untold others arrived from China on itineraries that first stopped in another country. While actual passenger counts for indirect fliers were not available, Sofia Boza-Holman, a spokeswoman for the Department of Homeland Security, said they represented about a quarter of travelers from China. The restrictions, she added, reduced all passengers from the country by about 99 percent.

Mr. Trump issued his first travel restrictions related to the virus on Jan. 31, one day after the World Health Organization declared the outbreak a global health emergency. In a presidential proclamation, he barred foreign nationals from entering the country if they had been in China during the prior two weeks. The order exempted American citizens, green-card holders and their noncitizen relatives — exceptions roundly recognized as necessary to allow residents to return home and prevent families from being separated. It did not apply to flights from Hong Kong and Macau.

About 60 percent of travelers on direct flights from China in February were not American citizens, according to the most recently available government data. Most of the flights were operated by Chinese airlines after American carriers halted theirs.

At a news conference about the restrictions, Alex M. Azar II, the health secretary, repeatedly emphasized that “the risk is low” for Americans. He added, “Our job is to work to keep that that way.”

Health officials also announced an expansion of the screening beyond arrivals from Wuhan. Dr. Robert R. Redfield, director of the Centers for Disease Control and Prevention, explained that people would be screened for “significant risk, as well as any evidence of symptoms.” If there was no reason for additional examination, “they would be allowed to complete their travel back to their home, where they then will be monitored by the local health departments in a self-monitoring situation in their home.”

The procedures called for screening to be conducted in empty sections of the airports, usually past customs areas. Passengers would line up and spend a minute or two having their temperature taken and being asked about their health and travel history. Those with a fever or self-reported symptoms like a cough would get a medical evaluation, and if they were thought to have been infected or exposed to the virus, they would be sent to a hospital where local health officials would take over.

Passengers would also be given information cards about the virus and symptoms. Later versions advised people to stay at home for two weeks.

In a statement on Thursday, the C.D.C. described the entry screening as “part of a layered approach” that could “slow and reduce the spread of disease” when used with other public health measures.

“We cannot stop all introductions,” the C.D.C. added, noting that the coronavirus pandemic was “especially challenging due to asymptomatic and presymptomatic infections and an incubation period of up to two weeks.”

Separately, on Friday, the Department of Homeland Security said in a statement that the administration’s measures were “unprecedented” and allowed “the U.S. to stay ahead of the outbreak as it developed.”

Passengers including Mr. Wu described a cursory screening process when they arrived in the United States.

Mr. Wu, who has had no symptoms and has not become ill, said he was told to stay inside for 14 days when he landed in Los Angeles. He said he received two reminder messages the next day by email and text, but no further follow-up.

Another traveler, Chandler Jurinka, said his experience on Feb. 29 had an even more haphazard feel. He flew from Beijing to Seattle, with stops in Tokyo and Vancouver.

At the Seattle-Tacoma airport, he said, an immigration officer went through his documents and asked questions unrelated to the virus about his job and life in China. At no point did anyone take his temperature, he said.

“He hands me my passport and forms and says, ‘Oh, by the way, you haven’t been to Wuhan, have you?’” Mr. Jurinka said. “And then he says, ‘You don’t have a fever, right?’”

Like others, he left the airport with a card that recommended two weeks of self-quarantine and a promise that someone would call to check up on him. He said he never got a call.

Other travelers also said the follow-up from local health departments was hit-or-miss. Some received only emails or texts.

Jacinda Passmore, 23, a former English teacher in China who flew into Dallas on March 10, after a layover in Tokyo, got a thorough screening at the Dallas-Fort Worth airport. It took about 40 minutes, she said, before she was cleared for her flight home to Little Rock, Ark.

State health workers later dropped off thermometers at her house and insisted her entire family stay home for two weeks and provide updates on their condition.

“They asked us every day: ‘Have you stayed inside? Have you met anyone? Have you been quarantined?’” Ms. Passmore said. “They’re really nice about it. They said, ‘If you need anything, we can go grocery-shopping for you.’”

Nineteen flights departed Wuhan in January for New York or San Francisco — and the flights were largely full, according to VariFlight. For about 4,000 travelers, there was no enhanced screening.

On Jan. 17,  from Wuhan, but only 400 more passengers arrived on direct flights before Chinese authorities shut down the airport. Scott Liu, 56, a Wuhan native and a textile importer who lives in New York, caught the last commercial flight, on Jan. 22.

Mr. Liu had gone to Wuhan for the Spring Festival on Jan. 6, but decided to come back early as the outbreak worsened. At the Wuhan airport, staff checked his temperature. On the flight, he and other passengers filled a health declaration form, which included questions about symptoms like fever, cough or difficulty breathing.

After they arrived at J.F.K. in New York, the passengers were directed to go through a temperature checkpoint. “It was very fast,” he said. “If your temperature is normal, they will just let you in.”

Mr. Liu said no one asked him questions about his travel history or health, and he received a card with information about what to do if he developed symptoms. At the time, there were no instructions to isolate. Mr. Liu said he and his friends all decided to do so anyway.

The charter flights began on Jan. 29.  one showed C.D.C. officials in full protective gear on the plane and escorting passengers after landing.

One group of passengers was eventually flown to Omaha to be taken by bus to a National Guard camp for quarantine. Video showed them accompanied by a full police escort, with lights flashing, helicopters overhead and intersections blocked off along the way.