ISTANBUL — Kurdish fighters in northeastern Syria withdrew from a flash-point city as part of a cease-fire agreement with Turkey, a spokesman said Sunday, a move that could ease tensions amid U.S.-led efforts to quell a spiraling conflict.

House Speaker Nancy Pelosi, meanwhile, led a surprise congressional visit to neighboring Jordan over the weekend, highlighting her sharp disagreement with President Trump’s decision to remove U.S. troops from northern Syria and Turkey’s subsequent attacks on Kurdish enclaves.

U.S. Defense Secretary Mark T. Esper, in Kabul on Sunday, said the cease-fire in northeastern Syria “generally seems to be holding,” despite reports of “intermittent fire.” He said the U.S. withdrawal was proceeding as planned.

Turkish President Recep Tayyip Erdogan had threatened to resume a military offensive in northeastern Syria if Kurdish fighters didn’t retreat from designated border areas by Tuesday evening, the deadline in the cease-fire pact.

Current and former national security officials criticized President Trump's hasty withdrawal from Syria on Oct. 20, saying Russia, Iran and ISIS will benefit. (The Washington Post)

A spokesman for the Kurdish-led Syrian Democratic Forces said they were keeping their end of the deal.

“As part of the agreement to pause military operations with Turkey. . . . Today, we have evacuated the city of Ras al-Ayn,” spokesman Kino Gabriel said. “We don’t have any more fighters in the city.”

Turkey’s offensive this month to rout Kurdish militants from the Syrian frontier has drawn international condemnation and set off a scramble for territory.

Vice President Pence traveled to Turkey last week to negotiate a halt to the fighting as U.S. troops stationed in northeastern Syria prepared to withdraw.

Sporadic clashes between the SDF and Turkish forces and their proxies in recent days in Ras al-Ayn, on the border with Turkey, threatened to undo the fragile agreement. Under the deal, Turkish forces would halt military operations for 120 hours to allow the SDF to retreat.

Turkey said Sunday that it was monitoring the evacuation of Kurdish militants it views as terrorists for their links to the Kurdistan Workers’ Party, or PKK, which has waged a decades-long insurgency against the Turkish state.

The Turkish Defense Ministry said Sunday that it had sent a 55-vehicle convoy to Ras al-Ayn. The ministry said a Turkish soldier was killed in an attack by Kurdish militants in Tal Abyad, about 75 miles west of Ras al-Ayn. 

Esper spoke to reporters traveling with him to Kabul, the Afghan capital.

“The U.S. withdrawal continues apace from northeast Syria,” he said. “Again, we’re talking weeks, not days.”

He said U.S. troops departing from Syria would go to western Iraq, where they would have two missions.

“One is to help defend Iraq and two is to perform a counter-ISIS mission as we sort through the next steps,” he said. “Things could change between now and whenever we complete the withdrawal, but that’s the game plan right now.”

Pelosi met with King Abdullah II and senior Jordanian officials Saturday night. Neither country released details of the talks until after the delegation departed for the United States on Sunday morning.

“With the deepening crisis in Syria after Turkey’s incursion, our delegation has engaged in vital discussions about the impact to regional stability, increased flow of refugees, and the dangerous opening that has been provided to ISIS, Iran and Russia,” Pelosi said.

Pelosi earlier called the cease-fire deal “a sham” that gave a pass to Turkey’s offensive at the expense of the Kurds, a key ally in the recent fight against the Islamic State in Syria.

Abdullah “urged a political solution that safeguards Syria’s territorial integrity and the unity of its people, while guaranteeing the safe and voluntary return of refugees,” according to the state-run Petra news agency.

Coverage of Pelosi’s “middle of the night” meetings in the Jordanian press focused largely on concerns that Turkey’s assault would result in the release of thousands of Islamic State fighters, many of them from Jordan, from Syrian prisons.

“This visit comes at a crucial time of threats to stability in the region and the control of ISIS,” the daily paper Al Ghad said.

Some saw Pelosi’s sudden appearance in Amman as a slap at Trump.

“I don’t think it matters what they talked about,” said a former Israeli general, who asked not to be named because of his ties to the military. “What matters is that she came here to draw a line under his abandonment of the Kurds and the outrage it has caused.”

Trump has said repeatedly that he wants to extract the United States from “endless wars” in the Middle East. The decision to move U.S. forces from Syria to Iraq highlights the challenges of reaching that goal.

The administration has sent thousands of troops to the region since the spring. The Pentagon said this month that 1,800 would deploy to Saudi Arabia to deter Iranian aggression.

 Trump, who often praises Saudi Arabia as an important ally, said the kingdom “has agreed to pay us for everything we’re doing to help them.”

On ABC News’s “This Week” on Sunday, Secretary of State Mike Pompeo defended the decision to withdraw U.S. troops from northeast Syria, saying the president “believes we’ve accomplished a significant part of our mission and he wants our folks to come home.”

“This was about getting a cease-fire and secure area, that this in fact would save lives in that space,” Pompeo said. “That was our mission set.”

Amanda Erickson and Tiffany Harness in Washington and Sarah Dadouch in Beirut contributed to this report.