With at least 78 dead and hundreds more feared missing after the sinking of a rusty trawler off Greece's Peloponnese peninsula Wednesday, questions are being asked if more could have been done to prevent the tragedy.

This is what we know so far:

 What the Greeks say

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 from 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 (1230 GMT to 1800 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.

At 2240 GMT, the trawler notified Athens of engine failure and it stopped moving. The nearby patrol boat "immediately tried to approach the trawler to determine the problem," the coastguard said.

Twenty-four minutes later, the Greek patrol boat skipper radioed in that the boat had capsized. It sank within 15 minutes at 2:19 am Greek time.

What survivors and critics say

There are mounting questions as to whether the Greek coastguard should have intervened earlier to escort the ageing trawler, clearly packed with people, to safety.

Government spokesman Ilias Siakantaris said there were unconfirmed reports that up to 750 people had been on the boat. Relatives and activists have told AFP that there were at least 125 Syrians were on board.

But the coastguard spokesman suggested 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 cooperation," he said.

Greece's leftist former prime minister Alexis Tsipras said -- after talking to survivors at the western port of Kalamata -- that the migrants had actually "called for help".

One video showed a survivor on Thursday telling Tsipras that the boat had capsized after the coastguard had attempted to drag it at excessive speed.

"So the Greek coastguard used a rope to drag you, and that is how you sank?" the leftist leader asked.

Government spokesman Siakantaris confirmed Friday that a rope had been thrown to "stabilise" the boat, but that the migrants had refused help, saying, "No help, go Italy."

"There was never an attempt to tie the vessel, neither by us nor any other ship," the coastguard spokesman said Friday.

Reber Hebun, a Syrian refugee based in Germany who travelled to Greece to find his 24-year-old brother Rukayan, passed on what his brother, who survived the disaster, had told him.

"The Greek coastguard did nothing to help them at the beginning, when they were close to them," he told AFP.

"A commercial boat gave out water and food and everybody rushed (forward). The boat became unstable at this moment," his brother told him.

What happened on board

Alarm Phone, which runs a hotline for migrants in distress at sea, said those on board had reported at 1520 GMT on Tuesday that the captain had fled on a small boat.

Fourteen minutes later, the migrants said that "the boat is overcrowded and... moving from side to side."

This is around the time the Greek coastguard said an English speaker on board had insisted the vessel was "in no danger" and did not require assistance.

The NGO also noted that migrants are reluctant to be intercepted by Greek forces owing to widespread reports of mistreatment and pushbacks, reports Athens consistently denies.

What rescue protocols say

Vincent Cochetel, special envoy of the United Nations High Commissioner for Refugees for the central and western Mediterranean, said Friday that Greece's argument for not intervening "does not hold up".

"Under international law, Greek authorities should have organised this rescue operation sooner, as soon as Frontex spotted the boat in distress," he told AFP.

"The boat was full to bursting... and the photos taken by Frontex leave no doubt that it was adrift and that people were objectively in a distress situation," Cochetel said.

Investigation and prevention

On Friday the UN called for "thorough" investigations into the "horrific tragedy".

UN rights office spokesman Jeremy Laurence said there was a need to investigate "people smugglers and human traffickers and ensure they are brought to justice", and that more broadly "there are a lot of questions that need to be asked".

The UN agencies for refugees and migrants called in a joint statement for "urgent and decisive action to prevent further deaths at sea".

They insisted states have an obligation to come together to address the dangerous gaps in search and rescue operations in the Mediterranean.