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Thousands of people being held in migrant detention camps with the prospect of deportation to Turkey have applied for asylum, Greek authorities said Tuesday, which could slow the rate of returns under a European Union-Turkey deal.

The European Union began sending back migrants Monday under an agreement with Turkey, but no transfers were planned Tuesday.

Maria Stavropoulou, director of Greece's Asylum Service, told state TV that some 3,000 people held in deportation camps on the islands are seeking asylum, with the application process to formally start by the end of the week.

Under the EU-Turkey agreement, those arriving on Greek islands from the nearby Turkish coast on or after March 20 are eligible for deportation if they do not apply for asylum or their application is rejected or inadmissible. They must be screened by asylum services before they are deported. Returns are starting with migrants who have not applied for asylum or whose claims are considered inadmissible.

Asylum applications typically take about three months to process, Stavropoulou said, but would be "considerably faster" for those held in detention.

"There will be a difficult few months ahead," she said. "We are dealing with people who speak 70 different languages and many have traveled to Greece without papers because they are escaping war."

Only 30 of 400 migration officers from other EU countries have arrived in Greece so far, Stavropoulou said, while additional locally hired staff would take "several months" to train and integrate into the Asylum Service.

More than 52,000 people have been trapped in Greece after Balkan and European countries shut their land borders to refugees and other migrants, and the EU forged the deal with Turkey.

Greece's asylum service said Monday it would be setting up an "emergency plan" for asylum applications in the next few weeks for the people in refugee camps across Greece.

"The Asylum Service is called on daily to document thousands of people as asylum applicants, something with far exceeds its objective abilities," it said in a statement.

On Monday some 202 migrants from 11 countries were sent back to Turkey, on boats from the Greek islands of Lesbos and Chios. In return as part of the agreement, dozens of Syrians were flown to Germany, Finland and the Netherlands on Monday and Tuesday.

It was unclear when the send-backs would resume.

The deal has come under harsh criticism from human rights groups and aid organizations, who question why Europe is sending potentially vulnerable people back to Turkey where they say their protection is not assured.

In Lesbos, about 200 people being held in the Moria detention center staged a sit-in protest Monday. The protesters, including several children, sat near the camp's fence, chanting "freedom, freedom."