By Missy Ryan and Phil Stewart

WASHINGTON (Reuters) - The death of Muammar Gaddafi after months of U.S. and NATO airstrikes may provide the Obama administration a needed foreign policy coup, but it is unlikely to alter the U.S. quest to keep Libya at arm's length.

Leaders of European nations that rallied support for a NATO campaign launched in March hailed the news Gaddafi had been killed in his hometown of Sirte on Thursday, capping months of bloody conflict between Gaddafi loyalists and Western-backed rebels.

That contrasted with the circumspect tone in Washington, where military leaders from the start voiced skepticism about a third war in a Muslim country and where budget woes fueled ambivalence toward involvement in a nation with scant U.S. interests.

President Barack Obama congratulated Libyans on the end to over 40 years of autocracy, but appeared to distance the United States as he placed the responsibility for Libya's future squarely on its people's shoulders.

"The American people wish the people of Libya the very best in what will be a challenging, but hopeful days, weeks, months and years ahead," Obama told reporters.

Yet after months of seeking a supporting role, Washington may be forced into the foreground if European nations do not provide robust support for what is likely to be a shaky political transition or if Libya descends into civil war.

"Ideally for the Obama administration, the Europeans should take the lead in developing a new regime, just as they did in bringing down the old one," said Kamran Bokhari, a security expert with the STRATFOR global intelligence firm.

"But there is a difference between what one wants and what one can actually get," he said. "Again, everyone's going to be looking at Washington."

Looming large in U.S. officials' minds is the violence that spiraled out of control in Iraq following Saddam Hussein's capture, trial and execution, which kept the United States in Iraq for years at great financial and human cost.

The Gaddafi government's downfall in August and now his death will go some way to validating what became known as the "Obama doctrine," in which Washington, unlike in Iraq and Afghanistan, played a more modest role rather than acting as de facto leader of an anemic coalition.

Following initial criticism for failing to act quickly in Libya, U.S. officials went to great lengths after the early weeks of the air campaign to make NATO the face of international military assistance for the ragtag rebel force.

Despite the Pentagon's heavy lifting on refueling, logistics and surveillance, nations like France and Britain embraced more forward-leaning military and diplomatic roles.

Still, given its military might, Washington may find itself playing an important role even after the NATO mission ends in providing training and other assistance to the new Libyan military or making use of its unique air assets.

MOTLEY LEADERSHIP

Perhaps the biggest question mark in determining the future U.S. role in Libya is the ability of its new leadership to stave off prolonged civil strife in an ethnically and tribally fractured country reeling after months of bloody conflict.

After Gaddafi's death, it remains unclear whether Libya's motley array of new leaders, with their diverse ideologies, can forge a unified path in a country new to democracy or whether remaining Gaddafi supporters will keep putting up a fight.

"Now more than ever, the risk of them not succeeding has increased as the one thing that hung everyone together is gone," Bokhari said.

Secretary of State Hillary Clinton articulated during a visit to Libya this week the widespread U.S. concerns about how well a host of militias can be streamlined into a single national army and about quickly establishing law and order.

Another obstacle for Libya, where Gaddafi commanded almost absolute power for decades, is its lack of strong government institutions that could smooth the path ahead.

"The success achieved thus far is very, very limited compared to the challenges that lie ahead," Les Gelb, an expert at the Council on Foreign Relations, told reporters.

Equally unclear is the precise nature of future U.S. nonmilitary involvement in the new Libya.

Since the conflict began, the United States has spent at least $135 million on humanitarian and other aid to Libya, a paltry sum next to the billions of dollars it has poured into rebuilding Iraq and Afghanistan.

The administration will likely aim to keep its financial support modest to an oil-rich country that already has billions of dollars in assets from the Gaddafi government at its disposal.

While Clinton promised to expand support for a nascent democracy, she vowed to find public-private funding for other initiatives like treating war victims in the United States.

As the Obama administration scrambles to stave off a budget crisis, the State Department also announced this week it had not sought new congressional funding for aid to Libya.

That could change if robust aid fails to materialize from Europe -- where political leaders are staring down their own fiscal crisis -- and if Washington feels aid could fend off a risky destabilization for a region already gripped by change.

There could be also be big U.S. commercial interest in a country where recent years of expanded foreign investment halted in February with the start of the uprising.

U.S. companies with operations in Libya include ConocoPhillips, Occidental and other firms involved in construction and oil field services.

"What U.S. business needs in any market is security and transparency and stability," said Chuck Dittrich, executive director of the U.S.-Libya Business Association. "I think this enables Libya to close the book on 40 years of a nightmare."

(Additional reporting by Arshad Mohammed, David Alexander, Doug Palmer, Glenn Somerville and Laura MacInnis in Washington and Andrew Quinn in Islamabad; Writing by Missy Ryan; Editing by Warren Strobel and Peter Cooney)