* Paris attacks focus minds as world leaders meet
* Obama vows redoubled effort against Islamic State
* European Council urges Russian cooperation against IS
* G20 set to agree that migration a global problem (Wraps previous G20 stories)
By Matt Spetalnick and Jan Strupczewski
BELEK, Turkey, Nov 15 (Reuters) - U.S. President Barack Obama vowed on Sunday to step up efforts to eliminate Islamic State in Syria and prevent it from carrying out attacks like those in Paris, while European leaders urged Russia to focus its military efforts on the radical Islamists.
Speaking at a G20 leaders summit in Turkey, Obama described the killings in Paris claimed by Islamic State as an attack on the civilised world and said the United States would work with France to hunt down those responsible.
The two-day summit brings Obama and fellow world leaders just 500 km (310 miles) from Syria, where a 4-1/2-year conflict has transformed Islamic State into a global security threat and spawned Europe's largest migration flows since World War Two.
"Traditionally the G20 has been a forum primarily to discuss economic issues facing the globe ... (but) the sky has been darkened by the horrific attacks that took place in Paris just a day and a half ago," Obama said in a statement after meeting Turkish President Tayyip Erdogan.
"The United States and its allies will redouble efforts to find a peaceful solution in Syria and prevent Islamic State militants from perpetrating attacks like those in Paris."
Obama and his Western allies now face the question of how the West should respond after Islamic State again demonstrated it posed a threat far beyond its strongholds in Syria and Iraq.
Washington already expects France to retaliate by taking on a larger role in the U.S.-led coalition's bombing campaign against Islamic State.
But European Council President Donald Tusk said Russia too should focus its military operations on Islamic State, rather than on the Syrian opposition battling President Bashar al-Assad, urging cooperation between Washington and Moscow.
"It should be our common aim to coordinate our actions against Daesh (IS) and for sure the cooperation between the United States and Russia is a crucial one," he said.
OBAMA-PUTIN HANDSHAKE
Russia joined the conflict a month and a half ago with air strikes in Syria, but has been targeting mainly areas controlled by the moderate Syrian opposition fighting Assad, its ally, rather than Islamic State, its critics say.
Turkey and Western allies, by contrast, want Assad out.
U.N. Secretary-General Ban Ki-moon said he welcomed the renewed sense of urgency to find a solution to the war in Syria after the Paris attacks, adding the world had a "rare moment" of diplomatic opportunity to end the violence.
Obama and Russian President Vladimir Putin have no formal bilateral meeting planned. As the leaders moved into place for a group photo on Sunday, Putin approached Obama and they shook hands, exchanging words for only a few brief moments.
Obama is also seeking to coax other European and Middle Eastern countries into more tangible steps to show their military commitment and will hold a bilateral meeting with Saudi Arabia's King Salman, U.S. officials said. In a call late last month, the two leaders affirmed the need to cooperate in fighting Islamic State.
Obama said he had also discussed in his meeting with Erdogan the progress made by foreign ministers in Vienna, who on Saturday outlined a plan for a political process in Syria leading to elections within two years, although differences over Assad's fate still remained.
MIGRATION CONCERNS
The coordinated attacks by gunmen and suicide bombers in Paris on Friday puts Obama and other leaders of the world's major economies under increased pressure to find common cause.
It remains to be seen, however, whether Washington itself has an appetite for much deeper involvement after already stepping up air strikes and committing small numbers of special operations troops to northern Syria to advise opposition forces in the fight against Islamic State.
The Paris carnage, in which 129 people were killed in attacks on a concert hall, restaurants, bars and a sports stadium, also poses a major challenge for Europe, with populist leaders rushing to demand an end to an influx of refugees and migrants from the Middle East and Africa.
In a diplomatic coup for Europe and for Turkey, the G20 leaders will agree that migration is a global problem that must be addressed in a coordinated way, according to a draft communique seen by Reuters, although it has yet to be accepted by all and is due to be published only on Monday.
Europe and Turkey, the most heavily hit by the crisis, had been pushing for the G20 to recognise the issue as a global problem and help to deal with it financially, despite opposition from China, India and Russia. A million migrants from the Middle East and Africa are expected to come to Europe this year alone.
According to a separate statement due to be released later on Sunday, a draft of which was also seen by Reuters, they also agreed to step up border controls and aviation security in the wake of the Paris attacks, which they condemned as "heinous".
The summit follows not only the Paris attacks but also comes two weeks after a suspected bomb attack on a Russian airliner killed 224 people in the Sinai Peninsula.
It also comes just over a month after two suspected Islamic State suicide bombers blew themselves up in Ankara, killing more than 100 people in Turkey's worst such attack.