Meanwhile, the United Nations said more than 1,000 people, most of them civilians, have been killed in Iraq so far this month, the highest death toll since the US military withdrew in December 2011.
Massoud Barzani, whose powerful minority bloc has long functioned as kingmaker in Iraqi politics, did not directly mention prime minister Nouri al-Maliki, who is facing the strongest challenge to his rule since he assumed power in 2006. But Mr Maliki has made little effort beyond rhetoric to win the trust of his critics, who are led by disaffected Sunnis, Kurds and even several former Shiite allies.
Instead, the Kurds have deployed their own security forces, known as peshmerga, and seized long-coveted ground of their own in the name of defending it from the al-Qaeda breakaway group and other Sunni insurgents who have swept through the north of Iraq.
Mr Kerry yesterday travelled to Irbil, the capital of the self-rule Kurdish region, a day after meeting with Mr Maliki and other Iraqi officials in Baghdad, where he pushed for them to adopt new policies that would give more authority to Iraq’s minority Sunnis and Kurds.
He said: “This is a very critical time for Iraq, and the government formation challenge is the central challenge that we face.”
Mr Kerry said after the Baghdad meetings that all the leaders agreed to start the process of seating a new parliament by 1 July, which will advance a constitutionally required timetable for naming a president, prime minister and a new Cabinet.
Mr Maliki’s political bloc won the most seats in parliamentary elections in April, but must assemble a majority coalition in the legislature to secure a third term for the Shiite leader.
Once a stable government is in place, it is hoped Iraqi security forces will be inspired to fight the insurgency instead of fleeing, as they have previously done in several cities and towns in Sunni-dominated areas.
Mr Barzani’s support will be crucial for resolving the political impasse because Kurds represent about 20 per cent of Iraq’s population and usually vote as a unified bloc.