By Adrian Croft and Alastair Macdonald
BRUSSELS (Reuters) - European Union leaders pledged to step up help for Tunisia on Friday, worried that an attack that killed 20 foreign tourists shows Islamic State militants spreading their influence from Libya and posing a growing threat to Europe.
EU governments are already deeply worried about chaos in Libya which has fueled an exodus of migrants that are putting a heavy strain on southern EU countries such as Italy.
Wednesday's attack in Tunisia, regarded in Brussels as a rare bright spot among countries swept up by the Arab uprisings, increased the EU's concern about threats to stability among its southern neighbors.
Islamic State claimed responsibility for the museum attack and Tunisia's government said the two gunmen had trained at a jihadist camp in Libya.
"Events in the southern Mediterranean are dangerous for Europe," European Council President Donald Tusk told a news conference after an EU summit.
"We have to offer everything we can to stabilize the situation in Tunisia. We can't say Tunisia is destabilized after this terrorist attack, but the risk is quite obvious that Tunisia will be the next step of activity and violence from Islamic State activists," he said.
Tusk said he had invited EU foreign policy chief Federica Mogherini to join him on a visit to Tunisia, Malta and Italy at the end of March.
In a statement condemning the Tunis attack, EU leaders pledged to intensify cooperation with Tunisia to counter terrorism, to strengthen Tunisia's democracy and to help with its economic and social development.
Italian Prime Minister Matteo Renzi said the attack in Tunisia was "new evidence that we are facing a global threat, the threat of terrorism. We need to concentrate our attention a bit more on the Mediterranean."
"It will be very important to help Tunisia also in terms of economic support so that it can face the negative impact on the tourism sector and on Tunisian GDP," Renzi told reporters.
EU leaders backed U.N.-brokered peace talks in Libya, where two rival governments and armed factions are battling for power and oil wealth four years after NATO helped oust Muammar Gaddafi. They urged all sides to quickly agree on a government of national unity, which the EU was ready to support.
German Chancellor Angela Merkel said Islamic State's influence in Libya was growing. "If the problems in Libya are not solved, the EU as a whole has a big problem," she said.
EU officials are drawing up proposals for a possible EU mission to Libya if the U.N. talks reach a deal. Mogherini has suggested a team of EU soldiers or civilians could monitor a ceasefire or protect airports and other infrastructure if the talks succeed, but EU member states are cautious about the idea.
(Additional reporting by Francesco Guarascio, Robin Emmott, Andreas Rinke, Tom Koerkemeier, Jan Strupczewski; Editing by Dominic Evans)