American forces continued their withdrawal from northern Syria Sunday and headed for Iraq, while efforts continued for a Kurdish evacuation from the area under the terms of the cease-fire agreed between the U.S. and Turkey.

Amid growing chaos after Turkey invaded the region earlier this month, Defense Secretary Mark Esper said late Saturday that all of the nearly 1,000 U.S. troops pulling out of northern Syria will now head to western Iraq to continue the campaign against Islamic State militants.

With President Donald Trump facing continued criticism for his approach to the crisis, the news means his vow to bring the troops home will seemingly go unfulfilled.

House Speaker Nancy Pelosi, a vocal critic of Trump's actions, is leading a congressional delegation to the region this weekend.

Kurds look to withdraw as Trump touts cease-fire

Vice President Mike Pence announced a five-day cease-fire in northern Syria Thursday after Turkey agreed to temporarily halt its advance to allow time for the Kurds to withdraw deeper into Syria.

Turkey has threatened to resume its offensive if the Kurds don't leave the zone near the border, claiming Sunday that there are "absolutely no impediments to withdrawal."

Meanwhile, the Kurds claimed that Turkey had blocked the opening of a safe corridor to evacuate.

But the Kurdish Rojava Information Center said Sunday that a convoy had successfully returned from the besieged border town of Ras al-Ayn with wounded civilians and fighters.

The evacuation of the town will be followed by a withdrawal of their forces from a broader section of the border with Turkey, a central requirement of the cease-fire deal.

The withdrawal is supposed to take place before Tuesday evening, when the pause in fighting is set to end.

Both sides have been accusing each other of violating the terms of the cease-fire and not following the agreement.

NBC News could not verify the claims.

Esper said Saturday that the fragile cease-fire was generally holding despite reports of intermittent fighting.

"We see a stabilization of the lines, if you will, on the ground," he said.

Trump has been steadfast about his decision to withdraw U.S. troops who'd been protecting Kurdish areas out of the way of the Turkish advance, prompting criticism both domestically and abroad.

The president has bragged about the cease-fire the U.S. negotiated, claiming it saved thousands of lives.

But a top Kurdish general told NBC News he fears the Turkish campaign in Syria will result in “ethnic cleansing.”

Gen. Mazloum Kobani, commander of the Syrian Democratic Forces, said that the U.S. bears full responsibility for what is happening.

“We trusted them for five years and the continuing war against ISIS, but now [there is] ethnic cleansing against the Kurdish people under their eyes. If they wanted, they would have interfered to stop it.”

The Kurds, a loyal ally in America's fight against ISIS for years, have claimed Trump’s actions amounted to a betrayal.

Pelosi in Jordan as U.S. troops head to Iraq

House Speaker Nancy Pelosi angrily walked out of a White House meeting Wednesday after she claimed Trump had a "meltdown" after contentious exchanges over Syria. It came as the House voted overwhelmingly to condemn Trump's withdrawal.

Pelosi led a bipartisan congressional delegation to Jordan Saturday to discuss the “deepening crisis.”

“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 in a statement.

The delegation included House Intel Chairman Rep. Adam Schiff and Rep. Mac Thornberry, a Republican and the ranking member on the House Armed Services Committee.

Meanwhile Esper told reporters en route to the Middle East Saturday that the U.S. withdrawal from northern Syria will take weeks, not days.

He said the mission for those troops would be to “help defend Iraq” and carry out a counter-ISIS mission. It is unclear whether the U.S. troops moving to Iraq will use it as a base to launch ground raids into Syria.

The additional U.S. troops would add to the more than 5,000 American troops already based in the country.

Turkey’s invasion of northern Syria has prompted fears of an ISIS resurgence and a worsening of the ongoing humanitarian crisis.

It has also seen Russia and forces of Syria's embattled President Bashar Assad make gains in the region after the U.S. withdrawal.