UPDATE 1-Obama: Leaner US Military Will Maintain Superiority

(Adds details, more Obama comment)

WASHINGTON, Jan 5 (Reuters) - President Barack Obama, rolling out a new defense strategy to shrink the country's armed forces at a time of tight budgets at home, pledged on Thursday to maintain the United States as the world's dominant military power.

"Our military will be leaner but the world must know - the United States is going to maintain our military superiority with armed forces that are agile, flexible and ready for the full range of contingencies and threats," Obama told a news briefing at the Pentagon.

Emphasizing the American presence in the Asia-Pacific region, where there is growing U.S. rivalry with an increasingly assertive China, Obama cautioned the military would remain vigilant in the Middle East.

U.S. troops last month completed their withdrawal from Iraq, which was invaded in 2003 to topple dictator Saddam Hussein, and are winding down their presence in Afghanistan.

Obama, focused on boosting economic growth and curbing stubbornly high U.S. unemployment as he fights for reelection in November, said that ending those two wars was an opportunity to rebalance national spending priorities after a decade of conflict.

Noting the defense budget had witnessed "extraordinary" growth after the Sept. 11, 2001 attacks on the United States, Obama said that pace of spending would slow but continue to grow.

"I firmly believe, and I think the American people understand, that we can keep our military strong - and our nation secure - with a defense budget that continues to be larger than roughly the next 10 countries combined," he said.

Obama has already earmarked defense budget cuts of $489 billion over 10 years. The defense budget faces an additional $600 billion in cuts after Congress failed to agree to broad deficit reduction after an August 2011 debt ceiling deal.

The president's budget proposal for 2013 will be published in early February.

"Some will no doubt say the spending reductions are too big; others will say they're too small," Obama said. "After a decade of war, and as we rebuild the sources of our strength - at home and abroad - it's time to restore that balance." (Reporting By Matt Spetalnick and Alister Bull; Editing by Paul Simao)