Iraq crisis: Fierce battles for Baiji and Tal Afar
Islamist-led militants and pro-government forces are engaged in fierce battles for the Baiji oil refinery and Tal Afar airport in northern Iraq.
Baiji, Iraq's biggest refinery, is surrounded by the rebels, who say they have seized most of Tal Afar airport.
The fighting comes a day after the US said it would send some 300 military advisers to help the fight against the insurgents.
President Barack Obama stressed that US troops would not fight in Iraq.
US Secretary of State John Kerry is expected to travel to Iraq soon to press for a more representative cabinet, hoping this could ease tensions between the country's rival Muslim sects.
The country's highest Shia religious authority, Grand Ayatollah Ali al-Sistani, has called for a new government to be set up quickly now the results of recent elections have been ratified.
He said a new government needed to aim for "broad national acceptance" and to "remedy past mistakes".
Correspondents say that will be seen by many as criticism of Iraqi Prime Minister Nouri Maliki.
Mr Maliki has been accused of pursuing anti-Sunni policies, pushing some Sunni militants to join the jihadist Islamic State of Iraq and the Levant (Isis), which has made rapid advances in recent days.
About 500,000 people have fled their homes in the country's second-largest city, Mosul, which Isis captured last week.
The UN estimates that that brings to about one million the number of people displaced within Iraq as a result of violence this year.
Analysis: John Simpson, BBC News, Baghdad
President Obama's statement wasn't the lifeline the Iraqi government had hoped for. They wanted immediate airstrikes to stop Isis in its tracks.
Instead, they will get up to 300 military advisers, who will restore the backbone to the Iraqi National Army which it has been missing since the Americans withdrew. The promise of air strikes is there, but attacks by US planes or missiles will, it seems, be dependent on some clear improvement in the way Iraq is governed - even though Mr Obama wouldn't say so.
He believes Prime Minister Nouri Maliki has endangered Iraq by ignoring Sunni concerns and governing in the interests of the Shia majority. Mr Maliki's supporters deny this and say he won't resign, but rivals to him are said to be emerging.
The least Mr Maliki will have to do is create a new and more inclusive government. Only then, perhaps, will the bombing start.
Isis says it has downed two military helicopters around the Baiji refinery but this has not been independently confirmed.
The BBC's Jim Muir in Irbil, northern Iraq, says it is thought the militants may have captured part of the vast oil complex.
They have also seized a disused chemical weapons factory in Muthanna, 70km (45 miles) north-west of the capital, Baghdad.
The US says it does not believe the site contains any material that the insurgents could use to make chemical weapons.
But state department spokeswoman Jen Psaki said: "We remain concerned about the seizure of any military site by" Isis.
Iraq has asked the US for air strikes against the Sunni militants.
Mr Obama said the US was prepared for "targeted and precise military action, if and when" required, but he insisted there was "no military solution" to the crisis.
He also pointedly urged the Shia-led Iraqi government to be "inclusive".
"The United States will not pursue military actions that support one sect inside of Iraq at the expense of another," Mr Obama said.
Isis in Iraq
Isis grew out of an al-Qaeda-linked organisation in Iraq
- Estimated 10,000 fighters in Iraq and Syria
- Joined in its offensives by other Sunni militant groups, including Saddam-era officers and soldiers, and disaffected Sunni tribal fighters
- Exploits standoff between Iraqi government and the minority Sunni Arab community, which complains that Shia Prime Minister Nouri Maliki is monopolising power
- Isis led by Abu Bakr al-Baghdadi, an obscure figure regarded as a battlefield commander and tactician
In addition to sending advisers, Mr Obama said that the US would be increasing intelligence efforts and setting up "joint operation centres in Baghdad and northern Iraq".
On Wednesday, the chairman of the US Joint Chiefs of Staff, Gen Martin Dempsey, warned that the US military still lacked sufficient intelligence to launch air strikes. He told a congressional hearing that pilots would have difficulty knowing who they were attacking from the air.
Iraq's sectarian split
- Sunnis and Shia share fundamental beliefs, but differ in doctrine, ritual, law, theology and religious organisation
- The origins of the split lie in a dispute over who should have succeeded the Prophet Muhammad as leader of the Muslim community
- Sunnis are the majority sect in the Muslim world, but Shia, most of them ethnic Arabs, form between 60% and 65% of Iraq's population; Sunnis make up 32-37%, split between Arabs and Kurds
- Sunni Arabs dominated Iraq under Saddam Hussein and their persecution of the Shia stoked sectarian tensions; the US-led invasion in 2003 gave the Shia an opportunity to seek redress
- Nouri Maliki has been accused of denying Sunni Arabs meaningful representation and pursuing security policies that target them