(AP) -- The president of Iraq's ethnic Kurdish region declared Tuesday 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.

"A united Iraq is a stronger Iraq," Kerry said in an interview broadcast on NBC's "Today" show Tuesday. He told ABC, "This is an opportunity for Iraq to come up with its own choice." Kerry also said that neither President Barack Obama nor the American people want a wholesale U.S. intervention in Iraq. And on CBS, he said the U.S. "is trying to move this process forward in what I think is a thoughtful, focused, disciplined way so that we have a structure in Iraq which will give us the greatest capacity for success."

Minority Sunnis who enjoyed far more authority and privilege under Saddam than any other sect have long been bitter about the Shiite-led government. And al-Maliki has been personally accused of targeting Sunni leaders whom he considers his political opponents.

Iraqi Kurds had no love for Saddam, and were allowed to carve out a semi-autonomous region in Iraq's north to protect themselves from his policies. But Barzani for years has feuded with al-Maliki, most recently over the Kurdish regional government's decision to export oil through Turkey without giving Baghdad its required share of the profits.

The Kurdish region is home to several vast oil fields, which have reaped security and economic stability unmatched across the rest of the Iraq.

Barzani's support is key to solving the current political crisis, because Kurds represent about 20 percent of Iraq's population and usually vote as a unified bloc. That has made Kurds kingmakers in Iraq's national political process.

Tuesday's meeting in Irbil, the Kurdish capital, came a day after Kerry traveled to Baghdad to discuss potential options with Sunni and Shiite leaders, including al-Maliki. Kerry said after the Baghdad meetings that all the leaders agreed to start the process of seating a new government by July 1, which will advance a constitutionally-required timetable for distributing power among Iraq's political blocs, which are divided by sect and ethnicity.

Once a stable government is in place, officials hope Iraqi security forces will be inspired to fight the insurgency instead of fleeing, as they did in several major cities and towns in Sunni-dominated areas since the start of the year.

U.S. special forces have been ordered to Baghdad to train and advise Iraqi counterterror soldiers. President Barack Obama is reluctantly sending American military might back to the war zone it left in 2011 after more than eight years of fighting.

Al-Maliki has for months requested U.S. military help to quell ISIL, and the Obama administration has said it must respond to the insurgent threat before it spreads beyond Iraq's borders and puts the West at risk of attack.

On Monday, Kerry said the U.S. is prepared to strike the militants even if Baghdad delays political reforms. After Tuesday's meeting with Barzani, Kerry departed for Brussels, where he and NATO foreign ministers will turn their focus to Ukraine and Afghanistan.

Early Tuesday, Iraqi authorities discovered the bodies of three men who were shot in the head and chest and had their hands and legs bound, a police officer said. The men, dressed in civilian clothes and believed to be their 30s, had been dumped in the streets of three Shiite neighborhoods in and around Baghdad.

A medical official confirmed the report. Both officials spoke on condition of anonymity as they were not authorized to release information.

The appearance of dead bodies in the streets is a grim reminder of sectarian violence that peaked in 2006 and 2007. During the worst of the bloodshed, Baghdad residents woke virtually every morning to find corpses, bearing gunshot wounds and signs of torture, that had been dumped in the streets or left floating in the Tigris River.

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Associated Press writers Sinan Salaheddin in Baghdad and Adam Schreck in Dubai, United Arab Emirates, contributed reporting.

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