It was a joke he repeated at many meals (southeast Turkey is home to that country’s Kurds). He was unfazed by the incessant artillery attacks. The next morning, we joined tens of thousands of Kurds fleeing the city for the Turkish and Iranian borders.

The United States military eventually established and supported a safe haven for the Kurds that became the nucleus of today’s de facto independent Kurdish state. Mr. Talabani quickly made friends with the American protectors, but the anger he had for Mr. Bush for failing to help stop Mr. Hussein’s troops during the uprising did not abate.

Under United States protection, the Kurdistan Region survived but did not thrive. This was partly because of the United Nations sanctions on Iraq, which applied to Kurdistan even though the region was not under Mr. Hussein’s control.

But Mr. Talabani and Massoud Barzani, another giant of the Kurdish cause, were also to blame. They were unable to make power-sharing arrangements work and fought a civil war from 1994 to 1998 that took thousands of Kurdish lives. As large as both men loom in the modern history of Kurdistan, the civil war is a black mark that many Kurds will not forget.

The prospect of remaking Iraq following the 2003 United States invasion brought Mr. Talabani and Mr. Barzani together in the job of writing a constitution that ensured the continuation of a self-governing Kurdistan and of a prominent Kurdish role in Baghdad. I advised both men in the negotiations, often suggesting ways to resist American pressure to give the federal government in Baghdad more authority. Mr. Talabani, who wanted to accommodate the United States when possible, sometimes bridled at my advice, more than once ribbing me by saying that I was “more Kurdish than the Kurds.”

Mr. Talabani’s jovial style sometimes led foreign diplomats to underestimate his resolve. He had no illusions about the brutality of the Shiite government that replaced Mr. Hussein. He complained about the Shiite death squads that fueled a Sunni-Shiite civil war, sometimes telling me that the Shiite government was not so different from the Hussein regime.

On Sept. 25, Kurdistan held a referendum to leave Iraq. Ninety-three percent of voters chose independence. Baghdad responded by closing Kurdistan’s airports and threatening to send troops to the border.

There is no long-term solution that can keep Kurdistan part of Iraq. But the Trump administration could take advantage of the shared grief among Iraqis by sending a high-level delegation to the country — perhaps led by Mr. Bush and Mr. Biden — that could bring the sides together to discuss a peaceful way forward. There could be no more fitting tribute to Jalal Talabani.