Greece paused deportations of migrants to Turkey on Tuesday, a day after the first boats took back 202 people under a controversial EU plan to cut off a migrant route to Europe.
Hundreds more are due to be removed later this week, but the migrants are arriving in Greece faster than they can be sent back.
More than 220 reached the Greek islands on Monday alone, according to the UN.
An increase in asylum claims has also reduced those eligible for deportation.
Under the EU deal with Turkey, migrants arriving illegally in Greece after 20 March are expected to be sent back to Turkey if they do not apply for asylum or if their claim is rejected.
For each Syrian migrant returned to Turkey, the EU is due to take in another Syrian who has made a legitimate request. Two Syrians were deported from Greece on Monday, while 32 were flown from Turkey to Germany and 11 to Finland on Monday. Another 31 Syrians arrived in the Netherlands on Tuesday.
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Although it was initially thought that none of the 202 migrants sent from Lesbos and Chios to the Turkish coastal town of Dikili on Monday had claimed asylum, the UN refugee agency (UNHCR) has revealed that 13 of them had expressed an interest but had not been registered by Greek authorities.
“We have expressed concern that this deal is being implemented before the necessary safeguards are in place in Greece and in Turkey, including that it’s being rushed – and is premature,” UN spokesman Boris Cheshirkov told the BBC.
He said the UN would now work with Turkey to ensure that the 13, including Afghans, would have their applications processed there.
Pope Francis is said to be considering a trip to Lesbos to highlight the difficulties faced by migrants and refugees there.
Although the visit has not been confirmed, the Greek Orthodox Church said it could take place late next week. The Vatican is understood to have approached the Church of Greece, which has also invited the head of the Eastern Orthodox Church, Ecumenical Patriarch Bartholomew.
Among the first deportees from Greece were 130 migrants from Pakistan, and a group of people mainly from Pakistan staged a protest on Tuesday at a detention camp on Lesbos, chanting “Freedom”.
A volunteer who had previously worked with the Pakistanis told the BBC that she felt many had legitimate claims for asylum but were worried they would be on the next ferries to Turkey.
Almost all the 3,000 people held in the Moria camp on Lesbos have now made applications, overwhelming the country’s asylum service.
Although 400 EU officials and 400 interpreters have been promised to help process the claims, only a handful have arrived on Lesbos so far, the BBC’s Sarah Rainsford reports. Another 62 asylum officers are due to arrive on Wednesday.
Processing of applications is likely to start on Thursday and is expected to take 48 hours. As anyone turned down for asylum has five days to launch an appeal, it could be well over a week before Greek authorities are able to resume deportations in large numbers.
EU border agency Frontex has been calling on EU member states to come forward with additional police officers and other staff to bring its mission in Greece up to strength.
in 2016, up to 30 March
37% of 2016 arrivals are children
53% arrive on Lesbos
366 died on Turkey-Greece route
853,650 arrivals in 2015
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.