The Trump administration signaled Monday it may re-thinking its troop withdrawal strategy in Syria, with the president and military officials now saying a small number of U.S. forces may remain in the country to protect oil supplies and keep them from falling into the hands of the Islamic State terror group.

The shift, which comes amid a fragile cease-fire in the battle between Turkey and the formerly U.S.-backed Syrian Democratic Forces (SDF), comes in the face of intense bipartisan criticism of Mr. Trump’s Syria policy from lawmakers, foreign policy analysts and retired military officials.

The president unexpectedly announced last week that the U.S. would move roughly 1,000 troops out of northeastern Syria as the Turkish advance gained steam, and military officials said that most of those forces are now on their way to Iraq.

The depth of the anger Syria Kurds felt about the U.S. withdrawal — leaving them exposed to a Turkish military incursion — could be seen in angry protests Monday targeting departing American troops, including a U.S. convoy hit by potatoes thrown by angry Kurds in the city of Qamishli.

It’s unclear how many troops, if any, would remain in that region of the country. Defense Secretary Mark Esper told reporters Monday that planning has just begun.

“There has been a discussion about possibly doing it,” he said during a press conference while traveling in Afghanistan. “There has been no decision with regard to numbers or anything like that.”

The administration last week negotiated a cease-fire between Turkey and the Kurdish-led SDF, which had been a key American ally in the fight against the Islamic State but a group that Ankara views as a terrorist threat. As the SDF last week redirected its forces to fight the Turkish military, there were widespread fears that ISIS could see a resurgence and could potentially recapture key territory in Syria, including valuable oil reserves in the eastern part of the country.

A key deadline looms Tuesday as a U.S.-brokered 120-hour cease-fire expires, with Turkey warning the fighting will resume if Kurdish fighters have not left a designated buffer zone Ankara has demanded just inside the Syrian border.

“If they don’t withdraw, our operation will re-start,” Turkish Foreign Minister Mevlut Cavusoglu said in Istanbul Monday.

A senior Kurdish official told the Associated Press that his forces are complying with the cease-fire and are completing the withdrawal of forces from along a section of the shared border with Turkey. Redur Khalil told the AP Monday that Turkish forces are violating the cease-fire, accusing its troops of shelling a village and carrying out military operations.

He said the Kurdish-led Syrian Democratic Forces are preparing to complete the withdrawal from the area between Ras al-Ayn and Tal Abyad towns, which flank the 75 miles covered under the cease-fire.

Mr. Trump on Monday stood by his decision to order a withdrawal, comparing the fight between the Kurds and the Turks to two kids in the lot fighting out old grievances. He told a Cabinet meeting Monday that Turkey has taken casualties, too.

“Plenty of Turks have been killed because of conflict on their borders. You have to look at both ways,” he said.

While many on Capitol Hill say the surprise U.S. withdrawal amounted to a betrayal of a faithful ally, Mr. Trump said the U.S. “never made a commitment to the Kurds,” and that he’ll “work something out so they have some money,” hinting at a deal with oil companies or some other kind of “cash flow.”

“We never agreed to protect the Kurds for the rest of their lives,” he said. “We’re not going to take a position. Let them fight themselves.”

Mr. Trump also explicitly said there’s “no reason” for American troops to remain Syria other than to “secure oil.”

Rising criticism

But critics showed no signs of easing up, blasting the oil field protection plan as another example of what they say is the president’s rash, incoherent foreign policy. Using U.S. forces to protect Syrian oil fields for the sake of making some sort of financial deal with the Kurds, they say, could be disastrous.

“A president shouldn’t talk like that, I’m sorry,” Brett McGurk, the administration’s former special presidential envoy in the fight against Islamic State, said Monday.

“This is the problem of not having a national security process,” he said during a panel discussion hosted by the Foundation for Defense of Democracies in Washington. “If you have a process before presidents say things, you would have some deliberation. We don’t want that oil to get in the hands of terrorists and other actors, but to say an American company is going to go in and exploit it, that raises serious illegal implications.”

Mr. McGurk announced his resignation last December shortly after the president first announced that the U.S. would withdraw its forces from Syria. Former Defense Secretary James Mattis also resigned over the decision.

Foreign policy analysts say there are other, broader problems with the plan to keep U.S. troops in Syria for the purposes of guarding oil fields. For starters, they argue that the SDF — which accused the president of undermining their cause when he pulled special operations forces away from the Syria-Turkey border ahead of the Turkish assault — simply no longer trust the administration.

“Trust in the Trump administration is now virtually non-existent,” said Charles Lister, director of the countering terrorism and extremism program at the Middle East Institute. “That some in Washington think another about-turn in policy allowing us to stay in negligible numbers, in a smaller piece of territory, would somehow enable us to sustain an anti-ISIS campaign and control Syria’s oil fields is nothing short of a fantasy. Perhaps after President Trump described Syria as ‘sand and death,’ some thought to appeal to his business bias by dangling the prospect of valuable oil resources to grab his attention.”

Observers also describe a growing humanitarian crisis in the contested Syrian zone. The aid group Save the Children said some 70,000 children have been displaced since the start of the Turkish offensive, and the UN estimates that more than 176,000 people have been uprooted.

It’s also become increasingly clear that the U.S. military’s popularity among the Kurdish-dominated in northeastern Syria is plummeting rapidly, raising questions about whether they could become targets if they remain in the country.

As the American convoy leaving the city of Qamishli was buffeted on Monday, protesters shouted “No America” and “America liar,” the Associated Press reported.

“Like rats, America is running away,” one protester yelled.

• Tom Howell Jr. contributed to this article, which is based in part on wire service

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