US Secretary of State John Kerry has arrived in Iraq's capital, Baghdad, as Sunni insurgents expand their control of towns across north-western Iraq.In Egypt on Sunday, Mr Kerry warned that Sunni militants Isis' "ideology of violence and repression is a threat not only to Iraq but to the entire region".
On Sunday rebels - spearheaded by Isis militants - captured border crossings to Syria and Jordan.
The strategically important airport in the northern Tal Afar has also fallen.
The town controls the main road from the Syrian border to Mosul, Iraq's second biggest city, which was captured by the rebels two weeks ago.
Officials said the rebels of the Islamic State in Iraq and the Levant took two key crossings in Anbar on Sunday, a day after seizing one at Qaim, a town in the province that borders Syria.
The capture of Tal Afar airport is a blow to the government as they were hoping to use it as a springboard to recapture the city of Mosul, says the BBC's Jim Muir in northern Iraq.
In other developments:
Police sources in Iraq have told the BBC 70 prisoners have been killed near the city of Hillah, south of Baghdad. The prisoners, who were all accused of terrorism, were being moved further south for security reasons when the convoy came under attack by gunmen. They were killed in the crossfire, several policemen were injured and six of the gunmen were shot dead, police said
Insurgents are reported to be taking control of a dam near the city of Haditha, the destruction of which would damage the country's electrical grid. The Iraqi military has sent reinforcements to the dam's site to protect it, reports say.
Analysis by Jim Muir, BBC News, in Irbil
The Iraqi government has lost all the crossing points into Syria and the only one into Jordan. Now Isis which is present there can connect up with its fellow militants on the Syrian side of the border. It is a very serious blow to the Iraqi government and it is important to have lost control of the borders symbolically as well as strategically.
Politically, it is a complete debacle, it is Iraq falling to pieces. The question is, can it be somehow pulled back from the brink? It was held together by Saddam Hussein, with a very tight dictatorial grip. Once that was broken, and all the mechanisms of control were destroyed and the Iraqi army disbanded, there was a move towards disintegration and chaos.
John Kerry is trying to persuade politicians to get their act together, to overcome sectarian differences and pull the rug from under the extremists of Isis. That is theoretically possible, but it needs Iran and America to co-operate - Iran is immensely influential with the Shia side - and at the moment it is not looking too good on that front after the latest statements from Tehran.
Since the fall of Mosul in early June, Isis have helped win large areas in the west and north.
They have taken four strategically important towns in the predominantly Sunni Anbar province - Qaim, Rutba, Rawa and Anah - in the last two days.
Gunmen were said to have captured the border posts of Walid, on the Syrian frontier, and Turaibil, on the Jordanian border, on Sunday after government forces pulled out.
The capture of frontier crossings could help Isis transport weapons and other equipment to different battlefields, analysts say.
Speaking in Cairo on Sunday, Mr Kerry urged Iraq's leaders "to rise above sectarian motivations and form a government that is united in its determination to meet the needs and speak to the demands of all of their people".
Iran's Supreme Leader Ayatollah Ali Khamenei said he opposed any US intervention, and accused Washington of "seeking an Iraq under its hegemony and ruled by its stooges".
"The main dispute in Iraq is between those who want Iraq to join the US camp and those who seek an independent Iraq," he said, dismissing talk of sectarianism.
The US, which pulled out of Iraq in 2011, is deploying some 300 military advisers to Iraq to help in the fight against the insurgents.