(Updates throughout)
By Lefteris Karagiannopoulos
ATHENS, March 3 (Reuters) - EU Council President Donald Tusk told illegal economic migrants on Thursday not to risk their lives or money to make a perilous trip to Europe "for nothing" but said unilateral actions by European Union states to deal with the crisis must stop.
Tusk was on a trip through Balkan states to try to drum up support for cohesion on how to deal with hundreds of thousands of migrants - a crisis that threatens to tear the bloc apart - before an EU summit on Monday.
From Greece, which has been a primary gateway of migrants flooding into Europe for more than a year, Tusk said anyone who was not a refugee should stay away.
"I want to appeal to all potential illegal economic migrants wherever you are from: Do not come to Europe. Do not believe the smugglers. Do not risk your lives and your money. It is all for nothing," Tusk said.
Up to 30,000 refugees and migrants have been stranded in Greece from progressive border closures further up the "Balkan corridor", the route taken to get into wealthier central and northern Europe.
"At Monday's summit, Greece will demand that burden sharing be equitable among all countries in the bloc, and sanctions for those that do not," Prime Minister Alexis Tsipras said after meeting Tusk.
"We ask that unilateral actions stop in Europe," said Tspiras in a view echoed by Tusk.
EU officials have told Reuters that European governments, and particularly Germany, are looking to Turkey to reduce the number of migrant arrivals in Greece to below 1,000 a day at most as an initial condition for discussing taking some Syrian refugees directly from Turkey said Greece would continue to do whatever it could to ensure no migrant or refugee was left helpless. But he added Greece could not bear the burden by itself.
"We will not allow Greece or any other country to be turned into a warehouse of souls," Tsipras said. "We are at a crucial moment for the future of Europe."
Greece would make every effort to apply international treaties. Speaking of the masses of people reaching Greek shores on small inflatable dinghies from Turkey, Tsipras said: "We will not push back people in the sea, risking the lives of children."
Officials said Tusk would be stressing in Athens and Ankara on Thursday that the goal was to eliminate entirely the transit of migrants from Turkey to Greece and that Europeans believed Turkey should be able to bring the numbers down to the "low triple digits" very soon.
"If there were to be a target figure, it would be zero," one EU official said, noting that 1,000 people a day would mean an unsustainable 350,000 people a year arriving in Greece.
(Editing by Richard Balmforth)