An "impulsive" decision by Turkish President Recep Tayyip Erdogan to invade northern Syria will further destabilize a region already caught up in civil war, and it puts America's Syrian Kurdish partners "in harm's way," Defense Secretary Mark Esper said Friday.

Washington is "greatly disappointed" by the Turkish incursion, Esper said at a Pentagon news conference, adding that the invasion has damaged relations with Turkey, a NATO ally. It also has raised the prospect of losing control of thousands of captured fighters.

Esper called on the Turks to halt their operation, which came after President Donald Trump pulled American troops from their positions near the border.

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"To be clear," Esper said, "we are not abandoning our Kurdish partner forces, and U.S. troops remain with them in other parts of Syria. The impulsive action of President Erdogan to invade northern Syria has put the United States in a tough situation."

Speaking alongside Esper, Gen. Mark Milley said the U.S.-backed Syrian Kurdish military known as the Syrian Democratic Forces, is still guarding the camps holding ISIS prisoners.

Milley, the chairman of the Joint Chiefs of Staff, said the Turkish military operations across the border into Syria are "still relatively limited." He also called on the Syrian Kurds to show restraint so that a diplomatic solution might emerge.

The remarks were the Pentagon's most explicit criticism of the Turkish operation, which began Wednesday as a campaign against the Syrian Kurd-led militia that has partnered with U.S. forces over the past five years to fight ISIS. The Pentagon had said before the operation began that the U.S. military would not support it, but it had not openly criticized the invasion.

President Donald Trump has called the invasion a "bad idea" and held out the possibility of the U.S. mediating a settlement.

He said in a tweet late Thursday, "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!"

....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! — Donald J. Trump (@realDonaldTrump) October 10, 2019

On Friday, Treasury Secretary Steven Mnuchin threatened sanctions against Turkey and said "we can shut down the Turkish economy if we need to."

Turkey's president said Friday his country "will not take a step back" from its offensive, defying serious warnings from the United States and other Western nations.

The Turkish government says it's clearing the area of terrorists. But more and more, it's starting to look like a campaign of ethnic cleansing – forcing the local Kurdish population away from cities and villages, CBS News' Charlie D'Agata reported.

The Turkish incursion has complicated U.S. military efforts in the region, even as Washington seeks to deter Iran from further attacks on Saudi Arabia following a drone and cruise missile assault in September that damaged key Saudi oil facilities. In response, the U.S. said it as deploying additional air defenses to Saudi Arabia.