With U.S.-backed forces poised to seize the last remaining stretch of Islamic State territory in Syria, Mr. Trump now is asking the Pentagon to retain several hundred Americans in northeastern Syria to help Kurdish fighters and at a small base in the south of the country, where they serve as an informal bulwark against Iranian influence.

After Mr. Trump spoke by phone Thursday with Turkish President Recep Tayyip Erdogan, the White House said the U.S. would keep about 200 American “peacekeepers” in Syria. By Friday, administration officials said the number would likely be higher than 200, and Pentagon officials referred to them as troops, not peacekeepers.

Mr. Trump said Friday his decision to abandon plans for a full withdrawal of U.S. forces from Syria was a recognition of the need to ensure that Islamic State doesn’t regroup.

“I’m not reversing course,” Mr. Trump said. “We can leave a small force along with others in the force, whether it’s NATO troops or whoever it might be, so that it doesn’t start up again. And I’m OK. It’s a very small, tiny fraction of the people we have.”

The U.S. currently has more than 2,000 troops in Syria, where they are helping the Kurdish-led Syrian Democratic Forces stamp out the last pocket of Islamic State resistance.

In December, Mr. Trump abruptly ordered the Pentagon to pull all U.S. forces out of Syria as soon as possible. The decision was made without consulting American allies and triggered the resignations of Defense Secretary Jim Mattis and Brett McGurk, the top State Department official leading the fight against Islamic State.

Since then, the U.S. has struggled to come up with a workable exit strategy. Turkey is seeking to create a buffer zone that would push back from its border Kurdish fighters that Ankara views as terrorists. France and the United Kingdom both said they would pull their troops out of Syria when the U.S. leaves.

Mr. Trump’s partial course reversal could pave the way for Paris and London to keep some troops in Syria alongside American counterparts. One senior administration official said he was optimistic that the president’s decision would lead to a shift from America’s European allies.

On Friday, French and British officials said they needed more information from the Trump administration before making any commitments to stay in Syria.

Securing European support is only one piece of the puzzle. The U.S. must still get buy-in from Turkey, which is pushing for creation of a 20-mile-deep buffer zone, and the Kurdish fighters looking to retain control of the rest of northeastern Syria.

Defense officials had begun to develop plans to keep some forces in Syria, particularly after Capitol Hill expressed its frustration with the withdrawal plan last month.

The Syrian Democratic Forces, which urged the U.S. to keep at least 1,000 troops in Syria, hailed Washington’s decision.

Gen. Joe Dunford, chairman of the Joint Chiefs of Staff, told reporters at the Pentagon that the forces would work with the Kurdish-led fighters in Syria to ensure that Islamic State, also known as ISIS, doesn’t rise again.

“We always had planned to transition into a stabilization phase, where we train local forces to provide security to prevent the regeneration of ISIS,” he said at the Pentagon before meeting with Turkish officials to discuss the ideas in detail.

The U.S. is seeking assurances from Turkey that its forces won’t attack Kurdish fighters in Syria, known as the YPG, who have led the American-backed fight against Islamic State. Ankara sees those forces as an arm of the Kurdistan Workers’ Party, better known as the PKK, which has waged a decadeslong fight inside Turkey for more minority rights and autonomy.

To speed up the campaign against Islamic State, Mr. Trump decided in 2017 to directly arm the YPG, with the understanding that the U.S. military would take back heavy weapons once the fight was over.

Gen. Joseph Votel, U.S. Central Command chief who oversees the fight against Islamic State, said earlier this week that he was exploring ways to continue arming and training the Syrian Democratic Forces after the fight to regain Islamic State-held territory is finished.

Other administration officials have been pressing Mr. Trump to keep some U.S. forces in Syria to counter Iran, which provides Syrian President Bashar al-Assad with vital military support. Officials didn’t explain what the U.S. military mission would be at a base in southern Syria.

Mr. Trump’s decision came after national security adviser John Bolton discussed the idea with the Pentagon and State Department, the senior administration official said. On Thursday, Mr. Bolton brought the plan to Mr. Trump, who agreed that a “couple hundred” troops should remain in Syria. The Pentagon was immediately notified, the official said.

The U.S. forces won’t serve as United Nations-style peacekeepers. They will instead monitor the Turkey-Syria border and try to prevent any clashes between the Turkish military and Kurdish forces in Syria. “The idea is to preserve the status quo” in northeastern Syria, the official said.

While the U.S. is now planning to keep several hundred troops in Syria, the military is still preparing to get most of its forces out of the country by the end of April.

Mr. Trump has said some of the troops in Syria could be shifted to neighboring Iraq so they could keep an eye on Iran. But that idea met resistance in Baghdad, where Iraqi leaders questioned that plan.

—Alex Leary, Vivian Salama and Courtney McBride contributed to this article.

Write to Dion Nissenbaum at dion.nissenbaum@wsj.com and Nancy A. Youssef at nancy.youssef@wsj.com