Since pulling out, American officials have expressed growing concern at the direction the Turkish incursion has taken, with officials warning on Friday that the United States would respond forcefully if Islamic State fighters were allowed to escape from prisons in the area.

On Friday afternoon, President Recep Tayyip Erdogan of Turkey vowed to continue the campaign.

“The West and the U.S., together they say, ‘You are killing the Kurds’,” said Mr. Erdogan in a speech. “Kurds are our brothers. This struggle of ours is not against Kurds. It is against terror groups.”

The Turkish government has framed the campaign as a counterterrorist operation because the Kurdish-led militia has close ties with a banned Turkey-based guerrilla movement that has waged a decades-long struggle against the Turkish state.

Mr. Erdogan has promised that the fight against the Islamic State will continue, and that his forces and their allies will continue to guard any captured militants in Kurdish-held prisons.

But the operation has already proved highly disruptive to efforts to keep the Islamic State at bay. Although American and Kurdish forces have defeated Islamic State militants in northeastern Syria, the group has sleeper cells in the region that could use the turmoil to retake the land they controlled in the early years of the Syrian civil war.

And the Kurdish militia has diverted soldiers to fight the invasion and abandoned joint operations with American troops as it prioritizes the defense of its land.

On Friday, a car bomb exploded on a residential street in Qamishli, the de facto capital of the Kurdish-held region — a rare act of Islamic State terrorism in a city that was relatively free of trouble before the Turkish assault began.