The Trump administration refused again Friday to recognize Iraq’s call to withdraw all U.S. troops, saying that any discussion with Baghdad would center on whatever force size the United States determines is sufficient to achieve its goals there. “At this time, any delegation sent to Iraq would be dedicated to discussing how best to recommit to our strategic partnership — not to discuss troop withdrawal,” the State Department said.

The statement came after Iraq’s caretaker prime minister, Adel Abdul Mahdi, said he had asked Secretary of State Mike Pompeo during a Thursday telephone call to begin talks about a “mechanism” to implement last week’s Iraqi parliamentary vote demanding the withdrawal of all foreign troops. “He didn’t quite characterize the conversation correctly,” Pompeo, speaking at a news ­conference, said of Abdul Mahdi’s description of the call.

“We are happy to continue the conversation with the Iraqis about what the right structure is,” Pompeo said. But the United States would continue its mission of fighting against the Islamic State and training Iraqi security forces. “As times change and we get to a place where we can deliver on what I believe and the president believes is our right structure with fewer resources dedicated to that mission, we will do so,” he said.

The public disagreement between the United States and its Iraqi ally, imperiling the mission of more than 5,000 U.S. troops in Iraq to fight the Islamic State, reflects tensions that have characterized the relationship for years, as well as the deep schisms in Iraqi politics.