In the strongest US statement yet against the attack launched on Wednesday, US Defense Secretary Mark Esper warned of "serious consequences" for Ankara if it does not halt the assault on Kurdish-led Syrian Democratic Forces positions in the area.

But US defense officials said there were so far no signs Turkey would halt its attacks.

"We oppose, and are greatly disappointed, at Turkey's decision to launch a unilateral, military incursion into Northern Syria, Esper said.

"This operation puts our SDF partners in harm's way. It risks the security of ISIS prison camps and will further destabilize the region," Esper said.

"The impulsive action of President Erdogan to invade northern Syria has put the United States in a tough situation."

Esper said he and Joint Chiefs Chairman Mark Milley had delivered that message to their Turkish counterparts in phone calls in the past 24 hours, but said it so far had shown no response from the Turkish side.

Esper said he "strongly encouraged" Turkey to stop the invasion in a phone call on Thursday with Turkish Defense Minister Hulusi Akar.

"I have yet no indication that they are willing to stop," Esper said Friday.

The incursion now in its third day has left so far dozens of fighters and civilians dead and sent 100,000 people fleeing their homes, according to a UN estimate.

Milley said Turkey has launched mostly air and artillery attacks on the SDF, a key US ally in the five year campaign to crush the Islamic State group but which Ankara considers an enemy for their support for Kurdish rebels inside Turkey.

"Right now the Turks have conducted airstrikes with fixed-wing, manned aircraft... they've conducted artillery strikes and some direct fire from tanks on the northern side of the border," Milley said.

"As far as forces that have come south, to our knowledge it's been relatively limited in terms of ground forces."

On Sunday, President Donald Trump appeared to give a green light to a Turkish invasion, announcing that Washington would pull back several dozen US special forces fighters positioned on the Syria-Turkey frontier.

Trump repeated this week that the Turks and Kurds have been battling for centuries but also warned Ankara not to do anything "off limits", while offering to "mediate a deal between Turkey and the Kurds."

Esper denied there had been and "green light" for Turkey to move, and noted that other partners in the NATO alliance had roundly condemned the incursion.

He stressed that US troops continue to work with SDF forces in areas away from the border region.

"We are not abandoning our Kurdish partner forces," he said.

But he also added that US troops would not get between the Turks and the Kurds in the fight.

Esper and Milley appeared determined to clear up mixed messages sent from Washington to the region since Trump said last Sunday he expected Turkish troops to begin attacking.

Democrats and Republicans in Congress have joined hands to threaten sanctions on Turkey if it launches a full assault on the SDF, which lost 11,000 fighters in the US-led campaign against Islamic State.