The president has not been clear on where his red lines sit, but a senior State Department official told reporters that indiscriminate attacks on civilians and ethnic cleansing of Kurdish areas would not be tolerated.
The official also stated that the objective at the moment was to work out a pause in hostilities.
"We have been tasked by the president to try to see if there are areas of commonality. To see if we can find our way to a ceasefire," the official said.
It remained unclear why the United States waited until after the Turkish invasion to try to mediate.
The US official also conceded that in previous talks, Turkey had rejected Washington's efforts at compromise, insisting instead on its "maximalist" positions of attacking the Kurdish-led forces.
Kurdish officials have said they complied with each request from the US, including removing defensive barriers along the border. They too blamed Turkey for not being satisfied with compromises offered by US diplomats.
"We think they are making a very big mistake," the official said about Turkey. "It has very big implications for all of our security," he said, adding that Ankara was endagering the fight against terrorism in the region.
"We will try our very best to get this thing stopped,"
Earlier Thursday, on Twitter, Trump said: "We have one of three choices: Send in thousands of troops and win Militarily, hit Turkey very hard Financially and with Sanctions, or mediate a deal between Turkey and the Kurds!"
Speaking with reporters, Trump said he was opposed to sending more troops into action.
Critics of the president say he paved the way for the current Turkish offensive in north-eastern Syria by abruptly pulling out some troops away from the border with Turkey.
Senators have been working on legislation to impose a slew of sanctions on Turkey over the invasion of northern Syria, amid outrage over the attack on the Kurdish-led Syrian Democratic Forces (SDF), the militia that worked with the US to defeat Islamic State.
Anger on Capitol Hill is being directed not only at Turkey, but also at Trump, who is being potrayed by a large number of lawmakers from both major parties as having abandoned the Kurds and the SDF, a key regional partner.
Turkey, a member of NATO, says it is fighting terrorists in Syria.
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