WASHINGTON — Senior Kurdish officials served notice on Thursday that Kurdistan would not participate in a new Iraqi government unless Baghdad grants it expanded autonomy and does not insist on reversing their occupation of Kirkuk.

“We are going to give once again a chance to the political process in Baghdad, but we are not going to think that is the only path,” said Fuad Hussein, the chief of staff to Massoud Barzani, the president of the Kurdish autonomous region.

“Parallel to that we are going to build ourselves, and we are heading toward exercising self-determination,” Mr. Hussein added before he went to the White House to see Vice President Joseph R. Biden Jr. and Antony Blinken, the deputy national security adviser.