By David Morgan

WASHINGTON (Reuters) - Republican lawmaker Paul Ryan, who caused an uproar this year by proposing to privatize Medicare, unveiled a new bipartisan approach on Thursday to cut costs in the government's $525 billion health plan for the elderly.

Ryan, chairman of the House of Representatives Budget Committee, joined Democratic Senator Ron Wyden of Oregon in a plan that would retain Medicare's popular fee-for-service program and allow private insurers to compete for more of its 48 million beneficiaries.

The plan would provide financial support allowing seniors to select insurance through a new, regulated exchange intended to foster competition and reduce costs.

Wyden and Ryan said they were raising the idea at the start of the 2012 election campaign as a way for Republicans and Democrats to find common ground to reform a popular program that has long been seen as politically untouchable.

"This is about trying to get out in front of this issue before it's just another high-decibel shouting match," Wyden said in an interview with Reuters.

"We're outlining a bipartisan approach that would give us a chance to have what might be characterized as an adult conversation about Medicare," he said.

Ryan faced fierce criticism from senior citizen groups early in 2011 with a plan to convert the entire Medicare program into a "premium support" system to help senior citizens buy private insurance.

Republican presidential candidate Newt Gingrich initially castigated the so-called Ryan plan as right-wing social engineering. Analysts said the public reaction undercut support for Republicans among senior citizens, a critical base of voters who had helped the party take control of the House from Democrats in 2010.

The new Wyden-Ryan plan would retain the premium support idea so that Medicare funds would help beneficiaries purchase private coverage vetted by federal health officials and sold through the exchange.

Insurers like UnitedHealth Group and Humana Inc already provide care for millions of beneficiaries through Medicare Advantage plans sponsored by the government.

The lawmakers said their plan would also impose a battery of consumer protection measures to ensure comprehensive and effective coverage.

"Our plan wouldn't merely ensure that American retirees have more health-care options than they have today. By allowing private plans to compete directly with traditional Medicare, our plan would also spur a wave of innovation to lower healthcare costs," Wyden and Ryan wrote in a Wall Street Journal opinion piece published on Thursday.

Beginning in 2022, the plan would allow Medicare spending to rise no higher than the growth in U.S. gross domestic product, plus 1 percent, they said. It would require Congress to cover any additional increases with measures including lower payments to healthcare providers and premium increases for higher-income beneficiaries.

Wyden said there were no plans to introduce legislation in the foreseeable future.

(Reporting by David Morgan; Editing by Michele Gershberg and Peter Cooney)