(Adds Kerry-Lavrov phone call)
By Mark Felsenthal and Patricia Zengerle
WASHINGTON, Aug 9 (Reuters) - U.S. President Barack Obama said on Saturday U.S. airstrikes have destroyed arms and equipment that Islamic State insurgents could have used to attack Arbil, the Iraqi Kurdish capital, but warned Americans it could take some time to end the crisis.
"I don't think we're going to solve this problem in weeks. This is going to take some time," Obama told reporters before leaving Washington for a two-week vacation in Massachusetts.
Obama said the United States would continue to provide military assistance and advice to the Baghdad government and Kurdish forces, but stressed repeatedly the importance of Iraq forming its own inclusive government "right now."
"I think this a wake-up call for a lot of Iraqis inside of Baghdad recognizing that we're going to have to rethink how we do business if we're going to hold our country together," he said.
Since an inconclusive general election in April, Baghdad has been in the grips of political deadlock, which has undermined efforts to combat the insurgents. Iraqi Prime Minister Nuri al-Maliki is under mounting pressure to abandon his bid for a third term in office but has shown little desire to step down.
Obama on Thursday authorized the U.S. military to make airdrops of humanitarian assistance to prevent what he called a potential "genocide" of the Yazidi religious sect in Iraq and conduct targeted strikes on Islamic State fighters who have been seizing territory in northern Iraq, a limited operation to protect Americans working in the country.
FIRST MILITARY ACTION SINCE 2011
It was the first direct U.S. military action there since Obama withdrew U.S. combat troops in 2011, and prompted concerns that Washington is getting involved in an open-ended Iraq project so soon after the costly and bloody war that began in 2003.
In a rare sign of agreement between Moscow and Washington, U.S. Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov concurred on the need to boost the Iraqi forces fighting the Islamist militants.
Kerry and Lavrov, in a phone call on Saturday, "agreed on the need to support the Iraqi Security Forces and the Kurdish forces in the fight" against the Islamic States, a senior U.S. State Department official said.
Obama said there had been two successful airdrops of food and water. He described next steps, including what would be a more complicated effort to create a safe corridor for the Yazidis to leave the arid mountain where they have been under siege by the Sunni Islamist fighters.
"American aircraft are positioned to strike (Islamic State) terrorists around the mountain to help forces in Iraq break the siege and rescue those who are trapped there," he said.
Obama emphasized that there are no plans to send in U.S. ground troops, again stressing the need for a unified government in Baghdad. "The most important timetable that I'm focused on right now is the Iraqi government getting formed and finalized," he said.
"We should have learned a lesson from our long and immensely costly incursion in Iraq," said the Democratic president, who made his opposition to the war launched by his Republican predecessor George W. Bush a key part of his first successful presidential campaign in 2008.
Obama said he spoke on Saturday with British Prime Minister David Cameron and French President Francois Hollande and they agreed to provide humanitarian assistance for Iraqi civilians.
The White House said Obama and Hollande talked about the need for a coordinated international response to the humanitarian crisis. The two also discussed U.S. airstrikes and agreed to work together on a longer-term strategy to combat the militant group, the White House said in a statement.
The Islamist militants have captured wide swaths of northern Iraq since June, executing non-Sunni Muslim captives and displacing tens of thousands of people.
Obama rejected any suggestion that he had withdrawn U.S. forces from Iraq prematurely, noting that it was Baghdad's decision not to allow troops to stay.
He said the Iraqi operations would not need the U.S. Congress to authorize additional funds for the moment, but he would make that request if it became necessary.
Congressional Republicans have backed Obama's willingness to bomb the militants and provide humanitarian aid, but questioned whether the president has an overall strategy for dealing with the Islamic State's advances.
The president has come under fire from some Republican lawmakers for leaving for his scheduled holiday on Martha's Vineyard while the crisis in Iraq rages, although he has taken fewer days of vacation to this point in his tenure than Bush.
While making his remarks, Obama was dressed in work clothes without a necktie. After speaking he returned to his residence before re-emerging with his wife and his eldest daughter, Malia, with whom he boarded a waiting helicopter.
Asked by a journalist if he was looking forward to his time off, he replied, "I'm ready to not have a suit on for a while."
Obama's approval ratings have slipped as he has faced a series of crises in his second term, including the bungled rollout of the Affordable Care Act health insurance law, the surge of child immigrants crossing the southwestern border illegally and renewed fighting in Iraq.
In one survey released in July by Quinnipiac University, respondents gave Obama the lowest approval ratings of any president in modern times. However, polling by Gallup has shown that while Islamic State successes in Iraq dented Obama's popularity, over the period between late April and mid-July, Obama's job rating increased to 43.2 percent from 42.4 percent, and has risen modestly for two quarters in a row. (Reporting by Patricia Zengerle and Mark Felsenthal; Editing by Sandra Maler, Frances Kerry and Mohammad Zargham)