By Phil Stewart and Steve Holland

WASHINGTON (Reuters) - U.S. Defense Secretary Chuck Hagel resigned on Monday, leaving under pressure as President Barack Obama faces critical national security challenges, including fighting Islamic State in Iraq and Syria and revising plans to exit Afghanistan.

It was the first major change to Obama's Cabinet since his Democrats were routed in midterm elections three weeks ago, and Republicans, who now control both houses of Congress, are looking for a new approach from the White house.

Hagel was appointed less than two years ago as Obama pushed his signature program of winding down wars in Afghanistan and Iraq, a process now being upended with U.S. re-engagement in Iraq and greater military cooperation with Kabul.

He had privately expressed frustration to colleagues at the administration’s strategy toward Iraq and Syria and at his lack of influence over the decision-making process, a source familiar with the situation said.

Officials said publicly the decision for him to leave was mutual but privately others said he was forced out. "There’s no question he was fired," said one source with knowledge of the matter.

Hagel raised questions about Obama's strategy toward Syria in an internal policy memo that leaked this fall saying the president's policy was in jeopardy due to its failure to clarify its intentions toward Syrian President Bashar al-Assad.

Obama has insisted the United States can go after Islamic State militants without addressing Assad, who the United States would like to leave power.

REPUBLICANS DEMAND CHANGE OF APPROACH

House Republican Speaker John Boehner said the change at the Pentagon "must be part of a larger re-thinking of our strategy to confront the threats we face abroad, especially the threat posed by the rise of ISIL (Islamic State)."

Senator John McCain, who is expected to become chairman of the Senate Armed Services Committee which will vet the new nominee, called for changes in Obama's defense policies.

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McCain, a fierce critic of the president, told Reuters Hagel had been "very unhappy" about micro-management from the White House and did not believe that Washington had a strategy to combat Islamic State.

Hagel will remain as Defense Secretary until his replacement is confirmed by the Senate. Congressional sources said it was almost certain that would not happen until after January, when Republicans take over and will control the confirmation process.

A Vietnam War veteran and longtime Republican senator, Hagel, 68, had been criticized by some for failing to clearly articulate policy, including during his confirmation hearing nearly two years ago.

He submitted his resignation letter after lengthy discussions with Obama that began in October, officials said.

Obama praised Hagel at a White House event called to announce his departure, saying he had always been candid with his advice and had "always given it to me straight".

Officials said Obama wanted fresh leadership during the final two years of his administration.

White House spokesman Josh Earnest said that when Hagel was appointed, the focus for the defense department was sorting out its budget and Islamic State was not an issue. Fighting the group would be the top priority for his successor, he said.

FLOURNOY IS POSSIBLE SUCCESSOR

Top potential candidates to replace Hagel include Michele Flournoy, a former under secretary of defense, and Ashton Carter, a former deputy secretary of defense, who were rumored to be contenders for Hagel's job before he was named.

Hagel, who was the only enlisted combat veteran to serve as defense secretary, ran into a wave of opposition when Obama, a Democrat, nominated him.

Republicans objected partly because Hagel opposed the 2007 'surge' of troops in the Iraq war, which eventually helped defeat al Qaeda and other militants and opened the way for a U.S. troop withdrawal.

He was seen as poorly prepared and hesitant during his confirmation hearing, including refusing to answer 'yes' or 'no' when McCain demanded he judge whether he was wrong to oppose the surge strategy.

Hagel, who became an outspoken critic of the administration of President George W. Bush, had also upset many in his party by endorsing Obama in his presidential race against Republican Senator John McCain in 2008.

Defense analyst Loren Thompson said Obama had seen Hagel as someone who could build bridges to the Republican Party, particularly in disputes over the massive defense budget, but Hagel’s ties were not in fact strong to begin with.

"What they need is a focused person who can clearly communicate with Capitol Hill on the need to loosen budget caps" that were damaging the military's ability to function, Thompson said. "Hagel seemed like he would appeal to both sides, but he wound up alienating Republicans and angering Democrats."

(Reporting by Phil Stewart, Steve Holland and Patricia Zengerle; Writing by David Storey; Editing by James Dalgleish)