* U.S. sees fragile gains, need for progress in Balkans
* Clinton seeks to buttress Bosnia, push EU membership
* U.S. wants Serbia, Kosovo talks to stabilize region (Adds violent, anti-gay riot in Belgrade)
By Andrew Quinn
WASHINGTON, Oct 10 (Reuters) - U.S. Secretary of State Hillary Clinton travels to the Balkans on Monday, seeking to buttress the fragile peace that was one of her husband&${esc.hash}39;s chief foreign policy achievements as president.
Clinton will urge reconciliation for Bosnia, Serbia and Kosovo, which battled through the collapse of Yugoslavia in the 1990s and dominated the news when former U.S. President Bill Clinton was in office.
For Hillary Clinton the Balkan puzzle is a familiar challenge -- although it is now she, and not her husband, who speaks for Washington as it attempts to bring the unstable region more closely into Europe&${esc.hash}39;s fold.
"She is on a family mission that hasn&${esc.hash}39;t been completed yet," said Janusz Bugajski, director of the New European Democracies project at the Center for Strategic and International Studies, a Washington think tank.
"They will not be able to say mission accomplished until all the loose ends are accounted for."
Bill Clinton helped engineer the 1995 Dayton accords that ended the Bosnian conflict and supported a NATO bombing of Serbia in 1999 that persuaded Belgrade to withdraw from Kosovo, an independence-minded former Serbian province subsequently placed under U.N. supervision.
U.S. Vice President Joe Biden made the Obama administration&${esc.hash}39;s first high-level visit to the Balkans in May 2009 and offered a fresh support for the region which saw the United States intervene twice militarily in the 1990s.
Strains persist, but analysts say Clinton&${esc.hash}39;s three-day visit to Sarajevo, Belgrade and Kosovo followed by NATO discussions in Brussels will show sustained U.S. commitment to putting the Balkan nations on track to join both the European Union and eventually the NATO alliance itself.
"This one trip won&${esc.hash}39;t achieve all of those things, but if it puts the Americans back into play that will be a good thing," said Daniel Serwer, a Balkan expert at the U.S. Institute of Peace.
A FUTURE IN EUROPE
Bosnia, Clinton&${esc.hash}39;s first stop, is widely regarded as the least stable part of the Balkans. Just completed presidential and parliamentary elections underscored the deep ethnic divides that still split the country some 15 years after the end of a conflict which killed 100,000 people.
Clinton will meet leaders including Bakir Izetbegovic, the moderate Muslim elected as the newest member of the country&${esc.hash}39;s trilateral presidency, to urge cooperation to advance political and economic reforms crucial to Bosnia&${esc.hash}39;s EU hopes.
"European Union and NATO membership (are) Bosnia&${esc.hash}39;s future, but to realize that future, leaders and parties and different ethnic groups are going to have to work together more than they have in the past," Philip Gordon, the assistant U.S. secretary of state for Europe, told reporters.
Izetbegovic wants fast progress on a constitutional reform that would speed EU membership. Clinton may also meet Bosnian Serb leader Milorad Dodik to drive home the point that Serb secession hopes are ill-advised, U.S. officials said. Dodik has not proved receptive to such a message from U.S. and European officials in the past.
Clinton will then travel to Serbia&${esc.hash}39;s capital, Belgrade, where she will meet President Boris Tadic and urge progress on the region&${esc.hash}39;s most unsettled ethnic puzzle, Kosovo.
Belgrade was hit by a violent riot on Sunday over a gay rights parade, with police battling gangs of nationalists and skinheads in a display of the intolerance that still marks Serbian society despite the government&${esc.hash}39;s drive to become more open.
While Kosovo is now recognized by the United States and most members of the EU, Belgrade has not given up its claim to the region, which many Serbs see as the cradle of their faith.
Serbia recently bowed to EU pressure and agreed to hold talks with Kosovo on issues such as transport, aviation and those still missing after the 1998-99 war in Kosovo, where thee population is 90 percent Albanian and 10 percent Serb.
The way forward is unclear, in part because Kosovo&${esc.hash}39;s president resigned in September, complicating the leadership question, and in part because of Belgrade&${esc.hash}39;s lingering reluctance to open substantive dialogue. (Editing by Jackie Frank and Christopher Wilson)
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