Turkey has warned the European Union that 3 million more refugees could flee fighting in Syria as the EU struggles to manage its biggest migration emergency in decades.

Around 2 million refugees from Syria are currently in Turkey, and tens of thousands of others have entered the EU via Greece this year, overwhelming coast guards and reception facilities.

EU Council President Donald Tusk told lawmakers Tuesday that "according to Turkish estimates, another 3 million potential refugees may come from Aleppo and its neighborhood."

"Today millions of potential refugees and migrants are dreaming about Europe," Tusk said at the European Parliament in Strasbourg, France.

He warned that "the world around us does not intend to help Europe" and that some of the EU's neighbors "look with satisfaction at our troubles."

Tusk also lashed out at countries for failing to fully respect EU asylum and border rules, naming Hungary, Italy, Slovakia and Greece.

"We have to respect commonly agreed rules," he said, adding that when countries say they intend to flout the laws "they undermine the essence of solidarity and our community."

Turkish President Recep Tayyip Erdogan held talks with senior officials in Brussels on Monday, and the EU's executive Commission was due to unveil later Tuesday a memorandum detailing the way the bloc and Turkey plan to cooperate on migration.

Erdogan has sought European backing for the creation of a safe haven and no-fly zone in northern Syria, saying that such moves are key to ending the refugee crisis.

Meanwhile, Austrian Chancellor Werner Faymann is heading to the eastern Aegean island of Lesbos with Greece's prime minister to view the impact of the refugee crisis and tour the facilities set up to handle the new arrivals.

Faymann and Greece's Alexis Tsipras are due on Lesbos around mid-day Monday and are to tour the reception center set up to register and process refugees and migrants.

About 400,000 people have arrived in Greece so far this year, most in small overcrowded boats from the nearby Turkish coast. The vast majority don't want to stay in the financially troubled country and head north through the Balkans to more prosperous EU states.

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Elena Becatoros in Athens contributed to this report.