KUALA LUMPUR, Malaysia—North Korea’s ambassador to Malaysia said the police investigation into the killing of Kim Jong Nam, half-brother of dictator Kim Jong Un, can’t be trusted and the incident will hurt diplomatic relations between the two countries.

“We cannot trust the investigation by the Malaysian police,” Kang Chol said on Monday outside North Korea’s embassy here.

Mr. Kang was summoned to the Malaysian Foreign Ministry earlier in the day to explain comments he made last week that Malaysia was hiding information on Mr. Kim’s death.

In addition, Malaysia recalled its ambassador to North Korea, escalating a diplomatic spat between the two countries.

At his news conference, Mr. Kang demanded that a joint investigation be conducted into the airport killing. He said North Korea has never identified the dead person by any other name than Kim Chol, which was the name on the diplomatic passport that Kim Jong Nam was carrying when he was attacked at Kuala Lumpur International Airport a week ago.

Malaysian Foreign Minister Anifah Haji Aman said the envoy’s accusations were “culled from delusions, lies and half-truth” and that embassies customarily “cooperate fully with the host government in order to ensure that the investigation is as thorough as possible.”

Mr. Kim was the oldest son of Kim Jong Il, the longtime dictator of North Korea who died in 2011.

The ambassador said the request for DNA samples from Mr. Kim’s family was preposterous, as North Korea had identified him as Kim Chol from his passport.

Malaysian police have yet to determine the cause of death and haven’t offered any evidence to incriminate the suspects, Mr. Kang said. He added that the Malaysian police investigation was being conducted with a political aim.

The incident is being politicized by Malaysia in collusion with South Korea, he said.

Malaysian Prime Minister Najib Razak, in response to the ambassador’s comments, said Malaysia has no reason “to paint the North Koreans in a bad light.” He said Malaysia’s police and doctors are “very, very professional” and Malaysia will be objective in applying the rule of law.

Mr. Kang alleged that Malaysian police officers beat the teenage son of a North Korean citizen who was arrested at his home in Kuala Lumpur late Friday. The plainclothes officers pointed guns at his family, he said.

“If each country holds fast its own laws, there will be no proper relations to be maintained and developed between countries,” Mr. Kang said.

A spokeswoman for the Malaysian police didn’t comment on the claims made by the North Korean ambassador.