* EU heads towards two crucial migration summits in March

* Rutte says Greece will get more EU help to deal with migrants

* Says Greek debt bailout must be separate from migration crisis (Adds detail, more quotes)

By Gabriela Baczynska

BRUSSELS, March 3 (Reuters) - Turkey must ensure the number of refugees and migrants leaving its shores for Europe drops towards zero, Dutch Prime Minister Mark Rutte said ahead of a meeting of EU and Turkish leaders on Monday.

The 28-nation bloc is pushing for more effective implementation of a deal under which Ankara is due to cut the number of arrivals and help alleviate what has turned into a major migration crisis for the EU.

"We need to bring it back to a level from which we can see zero. It has to be really considerably lower than it is today," Rutte, whose country holds the rotating EU presidency, said in an interview with Reuters and two other media outlets.

EU leaders are scrambling to prevent a repeat of the chaotic arrivals last summer, which has pushed Europe's cherished free-travel Schengen zone to the verge of collapse, raised security concerns and fuelled support for nationalists and anti-migrant groups across the bloc.

Rutte also called for an agreement to "accelerate readmission of third country nationals and economic migrants. I think that would be the minimum outcome."

He said Turkey had to do more to stop smugglers taking people on the short but perilous trip across the Aegean Sea to Greece. EU leaders and officials in Brussels have warned that the Monday summit and another one among EU leaders on Mar. 17-18 form the last chance to get the migration crisis under control.

"And I hope we can come to an agreement on resettlement: that, for a couple weeks, we can assess that the numbers coming from Turkey to Greece are really coming down, with the zero being visible, so that it is possible for the EU to start a more ambitious resettlement programme. So a minimum outcome and a preferred outcome."

BURDEN ON GREECE

After talks with Turkish Prime Minister Ahmet Davutoglu on Monday, the 28 EU leaders will themselves convene. Rutte said they had to agree that migrants be processed in Greece rather than allowed to trek north towards wealthier northern Europe.

The EU would then provide humanitarian aid and logistical support and help build shelters for people in Greece and start relocating them in larger numbers in exchange, Rutte said.

"I think we can get to reasonable decisions on all of this on Monday," he said.

Greece is the main point of entry for those fleeing war in the Middle East and has seen some 126,000 people arrive so far in 2016 after more than a million refugees and migrants reached Europe in 2015.

Some 25,000 refugees and migrants are estimated to be stuck in Greece, a major humanitarian challenge for a country recovering from an economic and debt crisis that nearly knocked it out of the euro zone.

Rutte said the latest euro zone's bailout conditions for Greece should not be loosened. "We should keep the two dossiers separate," he said.

He said EU leaders were repeatedly on the phone with Greek Prime Minister Alexis Tsipras to discuss Greece's needs and urging Athens to accept that Greece was the key migrant entry point.

"That's a fact of life and we have to deal with that, whilst at the same time ... acknowledging that we cannot leave Greece with the whole burden, we have to share." (Reporting by Gabriela Baczynska; editing by Philip Blenkinsop and Dominic Evans)