BRUSSELS — Their proclivity to divide, fight and break up was such that it became a verb — to balkanize. Now, the European Union wants to unite Balkan nations in the fold of a united continent, smothering any remaining enmity in cooperation and the promise of prosperity.

In one fell swoop on Friday, EU leaders welcomed Croatia as the club's newest member, agreed to open membership talks with Serbia and held out the promise of open trade and political cooperation with Kosovo.

After wars in the former Yugoslavia of the 1990s filled the rest of Europe with dread, EU leaders are slowly shedding their reticence and moving into one of the continent's most perilous areas.

"The European Union is courageous enough," said European Parliament President Martin Schulz at an EU summit in Brussels that wrapped up Friday.

Serbian President Tomislav Nikolic said the EU decision means that Serbia has restored its image abroad "even among those countries that do not like us very much."

"But all of them speak of Serbia with respect now," Nikolic said.

The prime minister of Croatia, which battled Serbia in the 1990s, welcomed the leaders' decision to give the go-ahead to talks with other Balkan nations.

"Their absence from the EU creates a sort of strategic gap in the European belly," Croatian Prime Minister Zoran Milanovic told reporters in Brussels, where he joined other leaders as an honorary guest. Croatia formally joins the EU on Monday after nearly a decade of negotiations.

He warned that Serbian membership is not a done deal.

"This process is going to be long and ... as anybody else they will have to play by rules," Milanovic said.

For would-be Balkan member states, a big part of the lure of EU membership is financial aid, jobs and investment. However, this appeal has faded because of the debt crises in the eurozone that have hurt trade with other economies in the region too.

The EU leaders agreed to open membership talks with Serbia by January, in recognition of its efforts to improve relations with breakaway Kosovo.

Challenges remain before former enemies can sit alongside each other at the same tables in Brussels to agree on joint security policies, for instance, and where to spend common funds.

Highlighting the gingerly walk toward peaceful coexistence, there were clashes Friday between Serbs and Albanians in Kosovo as Serbs celebrated Vidovdan, or St. Vitus Day, commemorating a medieval battle against invading Ottomans and symbolically asserting Serbian nationalists' claim to Kosovo.

France and Germany set the example for the continent by burying enmities and creating an economic union after World War II that was meant to render any new continental conflicts impossible.

After starting out as a largely western European group, the EU has steadily expanded east to bring in several nations that were once governed by communist regimes.

The Balkan wars of the 1990s, involving Croatia, Serbia, Bosnia and Kosovo, shattered the peace. Today the integration of Serbia and other countries that were involved in the conflicts is viewed as key for permanent and lasting stabilization and economic development of the region.

The former Yugoslav republic of Slovenia — which sees itself more as an Alpine nation than a Balkan one — joined the EU in 2004. Other countries in the region — Bosnia, Albania, Montenegro, Macedonia — are at different stages on the path toward possible EU membership.

Zoran Ostojic, a liberal lawmaker in the Serbian parliament, said the primary idea behind the integration "is stability of a region that has been unstable for centuries and which has produced more history than it can muster."

Ostojic said Balkan membership in the EU and NATO will "make the word balkanization vanish."

Despite lingering resentment of Serbia by some of its neighbors, "the region is also becoming aware how important it is for Serbia, as the biggest country in the region, to finally move faster toward EU integration," said Ognjen Pribicevic, a Belgrade analyst and a former ambassador to Germany. Pribicevic noted that both Croatia and Montenegro have promised to support Belgrade along the way.

Also Friday, EU leaders announced negotiations for closer ties with Kosovo, a possible step on the way to membership talks.

For both Serbia and Kosovo, the vital breakthrough came April 19, when the neighbors reached a historic agreement to normalize relations and end years of acrimony.

"There is remarkable progress," an upbeat German Chancellor Angela Merkel said. "Many problems have been overcome."

Kosovo, a former province of Serbia, declared independence in 2008. Over the years, Belgrade has said it would never recognize the sovereignty of Kosovo, considered by Serbia's nationalists to be the cradle of the country's medieval statehood and religion.

Kosovo has been recognized by over 90 countries including the U.S. and 22 of the EU's 27 members.

Merkel would not say whether formal recognition of Kosovo would be a prerequisite to Serbia's EU accession, noting that "it will take quite a long" time until that decision is due. She noted that negotiations with Croatia were opened in 2004.

Membership negotiations can take that long because any new EU nation has to bring reams of legislation into line with EU standards, from farm policy to human rights and legal issues. But Serbia is looking for the talks to take no more than five years.