Turkey has agreed to a ceasefire in northern Syria to let Kurdish-led forces withdraw.
The deal came after US Vice-President Mike Pence and Turkey's President Recep Tayyip Erdogan met for talks in Ankara.
All fighting will be paused for five days, and the US will help facilitate the withdrawal of Kurdish-led troops from what Turkey terms a "safe zone" on the border, Mr Pence said.
It is unclear if the fighters of the Kurdish YPG will fully comply, however.
Commander Mazloum Kobani said Kurdish-led forces would observe the agreement in the area between the border towns of Ras al-Ain and Tal Abyad, where fighting has been fierce.
"We have not discussed the fate of other areas," he said.
UK-based war monitor the Syrian Observatory for Human Rights (SOHR) said clashes were continuing in Ras al-Ain despite the ceasefire announcement.
It said 72 civilians had been killed inside Syria and more than 300,000 displaced over the past eight days.
What prompted the offensive?
Turkey launched the cross-border offensive last week, after US President Donald Trump announced he was pulling US forces out of the Syria-Turkey border region.
Its goal was to push back a Kurdish militia group - the People's Protection Units (YPG) - that Turkey views as a terrorist organisation.
Turkey had hoped to resettle up to two million Syrian refugees in the border area, but critics warned that could trigger ethnic cleansing of the local Kurdish population.
President Trump was accused by some of abandoning a US ally, as the Syrian Democratic Forces (SDF) - a group dominated by the YPG - fought alongside the US against the Islamic State (IS) group in Syria.
But on Wednesday he said the Kurds were "not angels", and declared: "It's not our border. We shouldn't be losing lives over it."
How has Trump reacted to the ceasefire?
Mr Trump tweeted about the Turkish ceasefire before his vice-president unveiled it, writing: "Millions of lives will be saved!"
He added later: "This deal could NEVER have been made 3 days ago. There needed to be some "tough" love in order to get it done. Great for everybody. Proud of all!"
Mr Pence credited Donald Trump's "strong leadership" during the announcement, saying: "He wanted a ceasefire. He wanted to stop the violence."
"I am proud of the United States for sticking by me in following a necessary, but somewhat unconventional, path," Mr Trump added on Twitter.
Just a day before the Pence-Erdogan meeting, it emerged that Mr Trump had sent his Turkish counterpart a letter about the offensive, urging him: "Don't be a tough guy. Don't be a fool!"
After the ceasefire announcement on Thursday, he called Mr Erdogan "a hell of a leader" who "did the right thing".
What does Turkey say?
Turkey's Foreign Minister Mevlut Cavusoglu told journalists the offensive would only be permanently halted when the SDF had left the border zone.
"We are suspending the operation, not halting it," he said. "We will halt the operation only after [Kurdish forces] completely withdraw from the region."
Mr Cavusoglu said Turkey had also secured its goal of having heavy arms removed from the Kurdish-led fighters, and their positions destroyed.
Mr Pence said the US would lift economic sanctions imposed on Turkey when the military offensive ended, and would not impose more in the meantime.
The reversal on sanctions was been strongly criticised by the two most senior Democrats in the US Congress.
Nancy Pelosi and Chuck Schumer described Turkey's suspension of hostilities as a "sham ceasefire", saying President Erdogan had given up nothing. They said the lifting of sanctions seriously undermined the credibility of US foreign policy.
Speaking to Al Arabiya, senior Kurdish politician Aldar Xelil said he welcomed an end to the fighting, but that the SDF would defend itself if exposed to violence.
James Jeffrey, the US special representative on Syria, acknowledged that Kurdish-led forces weren't happy about leaving their positions.
"We're basically doing our best efforts to get the YPG to withdraw using as a carrot and a stick the sanctions levers that we have," he told reporters.
"There's no doubt that the YPG wishes that they could stay in these areas."