But the US special envoy for Syria, James Jeffrey, said the agreement covered only a smaller area where Turkish forces were already operating, without giving details of how far along the border Washington believed it stretched.
Republican and Democratic senators accused Trump of having betrayed the Kurdish allies who were vital in fighting Islamic State group militants, of brushing aside the humanitarian costs of Turkey's invasion and of being outwitted by Ankara.
Turkish shelling hit in and around Ras al-Ayn on Friday morning, raising columns of smoke, seen by an Associated Press journalist in Ceylanpinar on the Turkish side of the border, but none was seen after 10.30am, and only sporadic gunfire was heard from inside the town.
Turkey says the "safe zone" would make room to settle up to 2 million Syrian refugees it is now hosting, and would push back the YPG militia which it deems a terrorist group because of its links to Kurdish insurgents in southeast Turkey.
"Sometimes you have to let them fight a little while", Trump said.
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Turkey's military crosses into Syria, targets SDF positions
Some 64,000 people have already reportedly fled their homes, the International Rescue Committee aid organisation said. Turkish Defense Minister Akar said a total of 342 "terrorists" had been killed in the incursion so far.
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The Britain-based war monitor said eight fighters of the Syrian Democratic Forces - the de facto army of the embattled Kurdish autonomous region - were killed in the strikes. Sent on the day Turkey launched its incursion into northeastern Syria, Trump in the letter said history risked branding him a "devil".
On Wednesday, Trump also spoke dismissively of the crisis, declaring the USA has no stake in defending Kurdish fighters who died by the thousands as America's partners against Islamic State extremists.
Trump has been accused of abandoning Kurdish-led fighters, Washington's main partners in the battle to dismantle Islamic State's self-declared caliphate in Syria, by withdrawing troops from the border as Ankara launched its offensive on October 9. Turkey views the Kurdish fighters as terrorists due to their links to an insurgency inside its borders.
The Trump administration had faced criticism for the perception that it abandoned its own allies: the Syrian Kurdish militias who partnered with the USA military to fight the Islamic State.
The Kurdish-led SDF had said they were ready to abide by the ceasefire in border territory between Ras al-Ain and Tal Abyad to its west. The Kurds responded to the announcement of the US withdrawal by effectively switching allegiances and have already invited forces of the Syrian government, backed by Moscow and Tehran, into towns and cities in areas they control.
'They fought for a few days and it was pretty vicious'.
Trump also acknowledged the fighting, but insisted that Erdogan had it under control. His staff told the BBC that he threw the letter into the bin and launched the Syrian operation the same day. The factory, situated between Kobani and Ain Issa in northern Syria, had served as the de facto headquarters for the American-led military effort.