Greece's merchant marine minister said Friday the survivors of the sinking of a migrant boat changed their accounts of the incident, initially saying the Greek Coast Guard saved them but later accusing it of badly mishandling the rescue operation.

Twelve people, mostly children, are believed to have perished in Monday's sinking. Only two bodies have been found.

The small fishing boat crammed with 28 people had entered Greece illegally from Turkey and the Coast Guard said it was towing the boat to a nearby Greek island when it capsized. The survivors said they were being taken back to Turkish waters.

International rights groups and Greek political parties, including the Socialist minority partner in the country's governing coalition, have called for a full investigation of the incident.

Survivors who arrived in Athens Thursday told TV news crews that the Coast Guard crew had ignored their pleas to take the women and children on their boat before the accident, and then allegedly stood by as passengers struggled in rough seas. The survivors claimed their boat was being led at speed to nearby Turkish waters to be abandoned.

Nils Muiznieks, the Council of Europe Commissioner for Human Rights, has said the incident "appears to be a case of a failed collective expulsion."

Speaking on Greek public television Friday, Merchant Marine Minister Miltiadis Varvitsiotis said the latest accounts were not the same as those made by survivors to Greek authorities immediately after the sinking.

"In their statements, a father who lost his companion and their four children states clearly that the Coast Guard saved us. A brother who lost his mother and three brothers states the same," he said, adding that the alleged change in accounts was "striking and curious."

European Home Affairs Commissioner Cecilia Malmstrom, in Athens for an informal meeting of European Union home affairs and justice ministers, pressed Greece to hold an independent investigation.

"It's a terrible loss of life of course," Malmstrom said, stressing that the details of the accident were still unclear. "I hope there will be an independent investigation to see what happened, who's possibly responsible, to establish all the facts."

Malmstrom noted that so-called pushbacks, in which migrants are forcibly and clandestinely returned to the country they started out from, are illegal.

"I note that there have been allegations of pushbacks," she said. "I presume that the government is looking into that."

Survivors of the boat sinking visited a makeshift basement mosque west of Athens for Friday prayers.

One survivor, Afghan Fadi Mohamed, lost his wife and three of his four children. He was helped to stand as he entered the site, looking visibly shaken. At the end of the hour-long service, the attendants filed past the survivors to pay their respects.

"We are asking for the members of our community to come forward and give evidence in any inquiry if needed," said Yunis Mohamed, head of the Afghan migrant community in Greece.

"This isn't the first time something like this has happened and it won't be the last — there has been a lot of violence against us at the Greek borders."

He added: "These people are still in shock. They haven't even started mourning yet."