Turkey's assault on Syrian Kurdish forces has not breached a red line declared by President Donald Trump, a US official said Thursday, as he added that Washington wanted to broker a ceasefire.

Trump, in a week of mixed messages, initially voiced understanding for Turkey before criticizing the offensive and warning of sanctions if the operation is not "humane."

Asked to define what actions would violate Trump's vague warning, the US official said they would include "ethnic cleansing... indiscriminate artillery, air and other fires directed at civilian populations."

"That is what we're looking at right now. We have not seen significant examples of that so far, but we're very early," the official told reporters on condition of anonymity.

He said that the operation launched Wednesday was not yet large-scale, saying the Turks "really have not engaged in great depth or in great numbers inside the border yet."

"That's one reason why we're issuing so many warnings, because we're very, very concerned about such indiscriminate firings," he said.

Trump has come under heavy criticism at home, even among usually steadfast Republican supporters, who say he abandoned US-allied Kurdish fighters who led the fight against the Islamic State group.

Smoke rises from the Syrian town of Tal Abyad after Turkish bombings
Smoke rises from the Syrian town of Tal Abyad after Turkish bombings AFP / BULENT KILIC

In a phone call on Sunday with President Recep Tayyip Erdogan, Trump -- a longtime critic of prolonged military involvements overseas -- said he was withdrawing US troops who had effectively served as a buffer preventing a Turkish incursion.

On Twitter on Thursday, Trump said that he hoped to "mediate a deal between Turkey and the Kurds" -- saying the alternatives were sending in "thousands of troops" or hitting Turkey hard with sanctions.

Asked to elaborate on the remarks, the US official said that Trump had asked diplomats to seek an end to the violence.

"We have been tasked by the president to try to see if there are areas of commonality between the two sides, if there's a way that we can find our way to a ceasefire," the official said.

He noted that Turkey in the past has reached ceasefires with the Kurdistan Workers' Party, or PKK, which has waged decades of separatist violence inside Turkey.

Erdogan as well as the Trump administration link the PKK to the Kurdish People's Protection Unit, or YPG, which dominates the Syrian Democratic Forces in Syria.

"That's the path that the president would most prefer to do -- a negotiated settlement," the official said.