With Mr. Trump standing by his side, Mr. Erdogan denounced Washington’s Syrian Kurdish allies and said he would never accept them as partners in the region. Mr. Erdogan suggested that the Syrian Kurdish group is a “clear and present danger” to Turkey and said “there is no place for the terrorist organizations in the future of our region.”

Mr. Erdogan’s comments came days after Mr. Trump approved plans to directly arm the Kurdish force in Syria, known as the YPG, that is working with U.S. special operations forces to push Islamic State from Raqqa, the militants’ biggest Syrian stronghold.

The two presidents expressed hopes of repairing the strained relationship between the U.S. and Turkey, two North Atlantic Treaty Organization allies. But the issue of arming the Kurdish fighters has cast a cloud over those efforts.

Mr. Erdogan and Turkish leaders view the YPG as an offshoot of the Kurdistan Workers’ Party, better known as the PKK, which has been fighting a decadeslong struggle for more rights and autonomy in Turkey, where Kurds represent about 18% of the population.

The U.S. and Turkey both classify the PKK as a terrorist organization, but disagree on the YPG. The U.S. views the YPG as a separate fighting force and doesn’t classify it as a terrorist group.

In the wake of Mr. Trump’s decision to arm the YPG, the U.S. plans to funnel antitank weapons, machine guns and ammunition to the YPG as they prepare to attack Islamic State in Raqqa.

Turkey has repeatedly accused the YPG of smuggling arms and fighters from neighboring Syria into Turkey. Last month, Turkey drew the ire of the U.S. by bombing YPG fighters in northern Syria, where U.S. special operations forces work side-by-side with the fighters.

Some U.S. officials worry that Mr. Erdogan could complicate the fight for Raqqa by attacking the YPG. In an effort to reassure Turkey, the U.S. is preparing to step up intelligence sharing with Ankara to help it in its fight against the PKK. After meeting with Turkey’s defense minister on Tuesday, Defense Secretary Jim Mattis said the U.S. plans to “increase cooperation on Turkey’s counter-PKK efforts.”

Turkey is a vital player in the fight against Islamic State. The country is home to Incirlik Air Base, which serves as a major launchpad for airstrikes against Islamic State.

Mr. Erdogan praised Mr. Trump’s election win and said the visit could usher in a new chapter for the two countries.

“I believe my current official visit to the United States will mark an historic turn of tide,” he said in Turkish through a translator. “We are laying the foundation of a new era.”

In his brief comments before Mr. Erdogan spoke, Mr. Trump made no mention of the YPG decision and said it was a “great honor” to welcome the Turkish president to Washington.

Mr. Trump expressed support for Turkey’s fight against the PKK and said he hoped the two countries could work more closely in confronting terrorist threats.

“Today we face a new enemy in the fight against terrorism, and again we seek to face this threat together,” he said.

The YPG dispute isn’t the only one straining relations between the U.S. and Turkey. Mr. Erdogan is also pressing the U.S. to extradite Fethullah Gulen, a reclusive Turkish cleric living in Pennsylvania that Turkey has accused of orchestrating last summer’s failed coup in Turkey.

Mr. Gulen has denied the allegations and the U.S. extradition process is expected to take years.

Since the July coup attempt, Mr. Erdogan has launched a sweeping crackdown on his opponents in Turkey. His government has closed scores of media outlets, detained more than 130,000 people and arrested nearly 50,000. Turkey now detains more journalists than any other country, according to the Committee to Protect Journalists.

Last October, as part of the post-coup crackdown, Turkish officials detained an American pastor, Andrew Brunson, who has led a ministry in the country for decades. In March, Mr. Brunson publicly urged Mr. Trump not to work with Turkey until he was freed. On Tuesday, a senior administration official said, Mr. Trump raised the issue with Mr. Erdogan in their private meeting.

Mr. Erdogan has consolidated power since the failed coup. Last month, Mr. Erdogan claimed victory in a disputed referendum that gives him expansive new powers as president.

In his statement, Mr. Trump made no comments on Mr. Erdogan’s crackdown in Turkey.