IRBIL, Iraq — The president of Iraq’s ethnic Kurdish region declared today that “we are facing a new reality and a new Iraq” as the country considers new leadership for its Shiite-led government as an immediate step to curb a Sunni insurgent rampage.

The comments by Kurdish President Massoud Barzani came as he met with visiting U.S. Secretary of State John Kerry, who is pushing the central government in Baghdad to at least adopt new policies that would give more authority to Iraq’s minority Sunnis and Kurds.

Kerry has repeatedly said that it’s up to Iraqis — not the U.S. or other nations — to select their leaders. But he also has noted bitterness and growing impatience among all of Iraq’s major sects and ethnic groups with the government of Prime Minister Nouri al-Maliki.

Barzani told Kerry that Kurds are seeking “a solution for the crisis that we have witnessed.”

Kerry said at the start of an hour-long private meeting that the Kurdish security forces known as peshmerga have been “really critical” in helping restrain the advance of the Islamic State of Iraq and the Levant, a Sunni insurgency that has overtaken several key areas in Iraq’s west and north, and is pushing the country toward civil war.

“This is a very critical time for Iraq, and the government formation challenge is the central challenge that we face,” Kerry said. He said Iraqi leaders must “produce the broad-based, inclusive government that all the Iraqis I have talked to are demanding.”

The U.S. believes a new power-sharing agreement in Baghdad would soothe anger directed at the majority Shiite government that has fueled ISIL. Iraq’s population is about 60 percent Shiite Muslim, whose leaders rose to power with U.S. help after the 2003 fall of former president Saddam Hussein, a Sunni.