“The Kurds — I don’t think they are coming back,” a senior Defense Department official said.

A senior White House official, asked whether the Obama administration viewed the independence of Kurdistan as inevitable, said: “I think that’s premature. Whatever one thinks of that prospect, now is not the time for another destabilizing event.”

But he added: “The way we’re thinking about it is, we’ve got to put out the fires first. Then we can think about the future of Iraq.”

Within the administration, Secretary of State John Kerry and his senior aides have spearheaded an effort to keep the Kurds inside a united Iraq.

And in an op-ed article last week in The Washington Post, Vice President Joseph R. Biden Jr. suggested that Sunnis, Kurds and Shiites form a new government on the basis of a “functioning federalism.” Iraq’s territorial integrity would be maintained, Mr. Biden wrote, but there would be an equitable sharing of revenue with Iraq’s provinces, and Iraqi communities would be allowed to maintain “locally rooted security structures.”

Such arrangements may address some of the Kurdish demands for autonomy, though some are so far-reaching that some American officials say they cannot be settled in the next few weeks and may need to be negotiated with Iraqi officials in Baghdad over a period of months, if not years.

The Kurds also have many supporters in Congress and among former officials, such as Gen. James L. Jones, a former national security adviser who is now the chief executive of the United States-Kurdistan Business Council. Last month, he was the host in Washington for two top Kurdish officials: Fuad Hussein, the chief of staff to Massoud Barzani, the Kurdish regional government president, and Falah Mustafa Bakir, the head of the Kurdish foreign relations department.