“We need them to stand down,” Mr. Pompeo said. “We need a cease-fire at which point we can begin to put this all back together again.”

But Mr. Erdogan said he had told President Trump that a truce was not possible because Turkey does not negotiate with “terrorists.”

Turkey has faced widespread Western criticism and threats of economic sanctions and arms embargoes because of the incursion, which aims to sweep Kurdish fighters away from the Turkish border.

But Mr. Erdogan has billed the incursion as necessary for his country’s security and as a way to get some of the millions of refugees to return to Syria.

On Wednesday, he said: “If, this very night, all terrorists leave their weapons, equipment, everything, destroy the traps they have set up and leave the safe zone we designated in the region from Manbij to the Iraqi border, then our Peace Spring operation, which only targets terrorists, will end by itself.”

The incursion began after Mr. Trump ordered United States forces to leave the region, paving the way for Mr. Erdogan to send in his troops and proxy militias. The decision also shattered a partnership with a Kurdish-led militia in Syria that had been essential to the international fight against the Islamic State and gave Russia an opportunity to fill the security vacuum.

The United States is now moving ahead with withdrawing the rest of its roughly 1,000 troops from northeastern Syria, opening a void that other combatants in the country’s eight-year-old war have sought to fill.