By Jeff Mason

WASHINGTON (Reuters) - President Barack Obama said on Thursday he is looking at all options to help the Iraqi government face down a growing insurgency from radical Islamists and does not rule out military strikes to bring security to the country.

"My team is working around the clock to identify how we can provide the most effective assistance to (Iraq)," he told reporters in the Oval Office.

"I don’t rule out anything because we do have a stake in making sure that these jihadists are not getting a permanent foothold in either Iraq or Syria," he said when asked whether the United States was considering air strikes to stop the violence.

Obama, speaking at the White House as he met Australian Prime Minister Tony Abbott, said the Iraqis needed to do more to bridge sectarian divides in the country, but he noted military action was needed right away.

"It’s fair to say that in our consultations with the Iraqis there will be some short-term immediate things that need to be done militarily, and our national security team is looking at all the options," Obama said.

"But this should be also a wakeup call for the Iraqi government. There has to be a political component to this.”

Iraqi Kurdish forces took control of the northern oil city of Kirkuk on Thursday, after government troops abandoned their posts in the face of a march by Sunni rebels toward Baghdad following their capture of the country's second city, Mosul.

Obama won the White House in 2008 largely on the back of his opposition to the U.S. war in Iraq. American troops returned home under his tenure and are preparing to leave Afghanistan, where the U.S. combat mission is slated to come to a close at the end of this year.

But critics, including Republican Speaker of the House of Representatives John Boehner, said Obama contributed to the unrest in Iraq by failing to negotiate a deal under which the United States would have left a small force there after pulling out troops at the end of 2011.

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Boehner urged Obama to deliver military and other aid promised to the government in Baghdad. “What’s the president doing? Taking a nap,” he said.

The potential for U.S. military intervention in the country alarmed some of Obama's fellow Democrats.

“I don’t think there’s any appetite in our country for us to become engaged in military activity in Iraq," said Nancy Pelosi, the House Democratic leader. "War begets war. It’s just not a good idea.”

But other lawmakers said they would support U.S. air strikes to help the Iraqi military.

"There is no scenario where we can stop the bleeding in Iraq without American air power. The Iraqi army is on the verge of collapse," Republican Senator Lindsey Graham told reporters after leaving a classified briefing for the Senate Armed Services Committee by U.S. Department of Defense officials.

"It's in our national security interest to intervene."

(Reporting by Jeff Mason; Additional reporting by Steve Holland, Roberta Rampton, Susan Cornwell, David Storey, and Patricia Zengerle; Editing by Eric Beech)