The UN's human rights chief has called for a clampdown on people smugglers as hundreds are feared dead after a boat carrying 750 migrants sank.
The fishing boat capsized and sank early on Wednesday about 80km from the southern coastal town of Pylos, with hundreds of women and children trapped in the vessel's hold.
Only 104 people have been rescued and subsequent searches have proved fruitless.
On Friday, the UN High Commissioner for Human Rights called for countries to take a tougher stance on human traffickers.
“What happened on Wednesday underscores the need to investigate people smugglers and human traffickers and ensure they are brought to justice,” said Jeremy Laurence, UN Human Rights Office spokesman.
“The High Commissioner reiterated his call to states to open up more regular migration channels and enhance responsibility sharing, ensure arrangements for the safe and timely disembarkation of all people rescued at sea and the establishment of independent monitoring and oversight of migration-related policies and practices.”
A charity is calling for an independent inquiry into the circumstances of the vessel's sinking, while it was being shadowed by the Greek coastguard.
Authorities, who were alerted by Italy on Tuesday and monitored the vessel over a period of 15 hours before it sank, say occupants on the vessel repeatedly refused Greek help, saying they wanted to go to Italy.
An advocacy group that had been in communication with the vessel said that people on board pleaded for help on at least two occasions.
The group, Alarm Phone, said it had alerted Greek authorities and aid agencies hours before the disaster unfolded.
Greek authorities have denied accounts that the boat flipped after the coastguard attempted to tow it.
“There was no effort to tug the boat,” coastguard spokesman Nikos Alexiou told state broadcaster ERT.
Refugee action group Alarm Phone, which operates a trans-European network supporting rescue operations, said their actions raise many questions and are calling for an inquiry.
“There are so many open questions regarding yesterday's mass shipwreck off Pylos. We need an independent investigation into the in/actions of the Greek forces,” it said.
“We demand that the search for the missing continues and that, before burial, DNA is taken of all bodies found.”
The Greek coastguard and government officials say their patrol boats and nearby cargo ships had been shadowing the fishing boat since Tuesday afternoon, after it was spotted by a surveillance plane operated by Europe's Frontex agency.
They said the trawler had briefly stopped to take on food and water from a Maltese-flagged ship, but that a person on board, speaking English through a satellite phone, had insisted that no further assistance was needed and that those on board wished to continue their journey to Italy.
“From 12.30 GMT to 18.00 GMT the merchant marine operations room was in repeated contact with the fishing boat. They steadily repeated that they wished to sail to Italy and did not want any contribution from Greece,” the coastguard said.
There are mounting questions as to whether the Greek coastguard should have intervened earlier to escort the trawler to safety.
“The fishing boat was 25 metres to 30 metres long. Its deck was full of people, and we assume the interior was just as full,” Mr Alexiou said.
He said the boat might have capsized earlier if they had attempted to intervene.
“You cannot divert a boat with so many people on board by force unless there is co-operation,” he said.
Since the incident, nine people, most of them from Egypt, have been arrested over the shipwreck on Thursday evening.
Authorities said they faced charges of negligent manslaughter, exposing lives to danger, causing a shipwreck and human trafficking.
Dimitris Chaliotis, a Hellenic Red Cross volunteer who was part of the rescue operations, said that most migrants were from Libya and Syria.
Greece is one of the main routes into the EU for refugees and migrants from the Middle East, Asia and Africa.
The UN has recorded more than 20,000 deaths and disappearances in the central Mediterranean since 2014, making it the most dangerous migrant crossing in the world.
About 3,800 people died on migration routes within and from the Mena region last year, the highest number recorded there since 2017, according to data published earlier this month by the International Organisation for Migration.