US President Donald Trump says he hopes to be able to mediate between Turkey and the Syrian Kurds, while also reiterating a threat to impose sanctions on Ankara.
"I hope we can mediate," Trump told reporters outside the White House on Thursday.
"We are going to possibly do something very tough with respect to sanctions and other things," he said, after indicating he wants Turkey to "take it easy".
Trump paved the way for the current Turkish offensive in north-eastern Syria by abruptly pulling out some troops on Monday and abandoning Syrian Kurdish fighters.
Earlier on 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.
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, the militia that worked with the United States to defeat Islamic State.
Earlier, the US warned Turkey it faces "consequences" if its assault against Kurdish militias does not protect vulnerable populations or contain Islamic State militants.
US ambassador to the UN Kelly Craft, speaking after a closed-door meeting of the UN Security Council on Syria, did not specify what those consequences could be.
Turkey pounded US-allied Kurdish militia in Syria for a second day on Thursday, forcing tens of thousands of people to flee and killing dozens.
"Failure to play by the rules, to protect vulnerable populations, failure to guarantee that ISIS cannot exploit these actions to reconstitute, will have consequences," Craft told reporters.
The 15-member Security Council met at the request of the five European nations: Britain, France, Germany, Belgium and Poland.
In a joint statement, the European states called on Turkey to stop its military action.