* Both sides say they hope ruling will mark watershed

* More than 130,000 people died during breakup of Yugoslavia

* Intent to destroy a population not proved - court (Updates with reaction)

By Thomas Escritt

THE HAGUE, Feb 3 (Reuters) - The United Nations' highest court ruled on Tuesday that neither Croatia nor Serbia had committed genocide against each other's populations during the wars that accompanied the violent breakup of Yugoslavia in the 1990s.

Both sides said they hoped the ruling would mark a watershed in relations, long since improved but still sometimes frosty.

Peter Tomka, president of the International Court of Justice, said the forces of both countries had committed crimes during the conflict, but that the intent to commit genocide -- by "destroying a population in whole or in part" -- had not been proven against either country.

"This marks the end of one page on the past, and I'm convinced we will start a new page on the future, much brighter and better," Serbian Justice Minister Nikola Selakovic told reporters in the Hague.

Croatian Foreign Minister Vesna Pusic said she hoped the ruling would contribute to "closing this historic chapter and moving on to a better and safer period for people in this part of Europe."

The cases were part of the long legal fall-out from the break-up of Yugoslavia into seven states in wars that lasted for much of the 1990s and left more than 130,000 dead in Europe's worst conflagration since World War Two.

Croatia, which joined the European Union in 2013, filed its case against Belgrade in 1999 and Serbia - a candidate for EU membership - its counter-case against Zagreb only in 2010.

"Croatia has not established that the only reasonable inference was the intent to destroy in whole or in part the (Croatian) group," Tomka said of Serbia's campaign to destroy towns and expel civilians in Slavonia and Dalmatia.

Rejecting Serbia's counterclaim, he said Croatia had not committed genocide when it sought to drive ethnic Serb rebels from the province of Krajina, and put hundreds of thousands of civilians to flight.

"Acts of ethnic cleansing may be part of a genocidal plan, but only if there is an intention to physically destroy the target group," Tomka said.

The panel of judges rejected Croatia's claim by fifteen votes to two. Serbia's counterclaim was rejected unanimously, implying that even Serbia's delegated judge had ruled against.

The U.N. tribunal for the former Yugoslavia, which also sits in The Hague, has long since ruled that genocide was committed in Bosnia, where more than 8,000 Bosnian Muslim men and boys were killed when the U.N. 'safe haven' of Srebrenica fell to Bosnian Serb forces in 1995.

In an earlier ruling from 2007 in a case brought by Bosnia, the ICJ found that Serbia was not responsible for genocide, but that it had breached the genocide convention by failing to prevent the massacre in Srebrenica. (Additional reporting by Ivana Sekularac in Belgrade and Zoran Radosavljevic in Zagreb; Editing by Matt Robinson and Andrew Heavens)