US Secretary of State John Kerry has arrived in the northern Iraqi city of Erbil to hold talks with Kurdish leaders as Sunni rebels continue their offensive.

John Kerry’s trip comes a day after he visited Baghdad and pledged US support for Iraqi security forces.

He said Iraq faced a moment of great urgency as its very existence was under threat.

The Sunni rebels say they have fully captured the country’s main oil refinery at Baiji, north of Baghdad.

Secretary of State John Kerry has arrived in the northern Iraqi city of Erbil to hold talks with Kurdish leaders

John Kerry’s meetings with Kurdish leaders come as Iraqi Kurdish President Massoud Barzani strongly suggested that his region would seek formal independence from the rest of Iraq.

Speaking on Monday, John Kerry said Iraq’s PM Nouri al-Maliki and other leaders had committed themselves to the “essential ” step of forming an inclusive unity government by the end of the month.

Insurgents, spearheaded by Islamists fighting under the banner of the Islamic State of Iraq and the Levant (ISIS), have overrun a swathe of territory in the north and west including the second-biggest city, Mosul.

They are bearing down on a vital dam near Haditha and have captured all border crossings to Syria and Jordan.

The Baiji refinery, in Salahuddin province, had been under siege for 10 days, with militant attacks repulsed several times. The complex supplies a third of Iraq’s refined fuel and the battle has already led to petrol rationing.

A rebel spokesman said it would now be handed over to local tribes to administer, and that the advance towards Baghdad would continue.

Speaking at the US embassy in Baghdad, John Kerry said US support would “allow Iraqi security forces to confront [ISIS] more effectively and in a way that respects Iraq’s sovereignty”.

“The support will be intense, sustained, and if Iraq’s leaders take the steps needed to bring the country together it will be effective,” he said.

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