US Secretary of State John Kerry has told the BBC there must be regional unity to expel Sunni rebels from the Isis group who have taken large swathes of northern and western Iraq.
He said there was no military solution, stressing the need for a new Iraqi government that empowered people in communities where Isis had taken hold.
Mr Kerry has been talking to Kurdish leaders in the northern city of Irbil.
The rebels continue to advance, and are fighting to take a key oil refinery.
The insurgents, spearheaded by Islamists fighting under the banner of the Islamic State of Iraq and the Levant (Isis), have overrun much of north and west Iraq, including the second-biggest city, Mosul.
Meanwhile, a United Nations human rights team in Iraq reported that at least 1,075 people were killed in Iraq so far in June, most of them civilians.
The UN said the figures, which include a number of verified summary executions, should be viewed as an absolute minimum.
‘No military solution’
In an interview with the BBC’s Kim Ghattas, Mr Kerry said: “Every country in the region will combine in order to take on and expel Isis because it is simply unacceptable to have a terrorist organisation grabbing territory and challenging the legitimacy of governments.”
When asked about military action, Mr Kerry said the Kurdish leaders had agreed there was “no military solution”.
He said: “There may be military action but there has to be a political solution that deals with empowering the people in the communities where Isis is today.
“Just a strike alone is not going to change the outcome – you need to have a full-fledged strategy… which is principally a political strategy.”
Mr Kerry said he had come away from his two days of talks – in Baghdad and Irbil – appreciating a sense of urgency and commitment among Iraqis to tackle the crisis.
But he said: “Words are cheap. We know that. So it’s actions that will matter.”
Mr Kerry’s meetings with Kurdish leaders came as the Kurdish region’s President Massoud Barzani strongly suggested that it would seek formal independence from the rest of Iraq.
In a CNN interview, he said: “Iraq is obviously falling apart… The time is here for the Kurdistan people to determine their future and the decision of the people is what we are going to uphold.”
Mr Kerry told the BBC he did not regard the Kurdistan region as separate and stressed that the US believed a “united Iraq is a stronger Iraq”.
Jim Muir, BBC News, Irbil
It’s been a really to-and-fro battle for the Baiji refinery. The capture of the complex would enable the rebels to supply Mosul with energy, which is seen as vital to the viability of the region they are carving out.
Meanwhile, extremely concentrated political efforts are going on behind the scenes to get the politics in Baghdad right.
Only then would America wade in and start doing anything physical. There are urgent efforts to get parliament to meet on time on 1 July and to agree in advance who will be the new PM. Everybody I speak to says this will not be Nouri Maliki but one of about three other figures acceptable to Iran and America, which has a key role to play in trying to broker a deal.
Iraqi Prime Minister Nouri Maliki, a member of Iraq’s Shia Muslim majority, has been criticised for concentrating power among his mostly Shia allies and excluding other groups including Sunni and Kurdish communities.
The US, which pulled out of Iraq in 2011 after eight years of occupation following the 2003 invasion that toppled President Saddam Hussein, has already announced it is deploying some 300 military advisers to Iraq to help fight the insurgents.
The rebels say they have now fully captured the country’s main oil refinery at Baiji, north of Baghdad.
However, Iraqi officials said there was still fighting at the site and that troops were holding off the insurgents.
The refinery, in Salahuddin province, has 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.
The AFP news agency quoted officials as saying that Iraqi air strikes near Baiji town on Tuesday had killed at least 19 people, with other air strikes on Husseibah in the west.
Reuters quoted Iraqi officials as saying rebels had attacked the huge al-Bakr air base, north of Baghdad.
They are also fighting for control of key border crossings in Anbar province that link Iraq with Syria, pursuing their goal of forming a “caliphate” straddling both countries.
Iraqi media on Tuesday reported that US drones had struck Isis bases at the al-Qaim crossing, but the Pentagon said the US had not hit any targets on the Iraq-Syria border. Earlier reports said Syrian warplanes had bombed the area.
There were also conflicting reports over who controlled the Walid border crossing with Syria and the Traybil crossing with Jordan.
On Tuesday morning, Sunni tribes aligned with Isis said they had seized the crossings, but Iraqi military spokesman Lt Gen Qassim Atta told a news conference in Baghdad they had been “fully recaptured” by security forces.