The hull of the fishing trawler lifted out of the water as it sank, catapulting people from the top deck into the black sea below. In the darkness, they grabbed onto whatever they could to stay afloat, pushing each other underwater in a frantic fight for survival. Some were screaming, many began to recite their final prayers.

"I can still hear the voice of a woman calling out for help," one survivor of the migrant boat disaster off the coast of Greece told CNN. "You'd swim and move floating bodies out of your way."

With hundreds of people still missing after the overloaded vessel capsized in the Mediterranean on June 14, the testimonies of those who were onboard paint a picture of chaos and desperation. They also call into question the Greek coast guard's version of events, suggesting more lives could have been saved, and may even point to fault on the part of Greek authorities.

Rights groups allege the tragedy is both further evidence and a result of a new pattern in illegal pushbacks of migrant boats to other nations' waters, with deadly consequences.

This boat was carrying up to 750 Pakistani, Syrian, Egyptian and Palestinian refugees and migrants. Only 104 people have been rescued alive.

CNN has interviewed multiple survivors of the shipwreck and their relatives, all of whom have wished to remain anonymous for security reasons and the fear of retribution from authorities in both Greece and at home.

One survivor from Syria, whom CNN is identifying as Rami, described how a Greek coast guard vessel approached the trawler multiple times to try to attach a rope to tow the ship, with disastrous results.

"The third time they towed us, the boat swayed to the right and everyone was screaming, people began falling into the sea, and the boat capsized and no one saw anyone anymore," he said. "Brothers were separated, cousins were separated."

Another Syrian man, identified as Mostafa, also believes it was the maneuver by the coast guard that caused the disaster. "The Greek captain pulled us too fast, it was extremely fast, this caused our boat to sink," he said.

The Hellenic Coast Guard has repeatedly denied attempting to tow the vessel. An official investigation into the cause of the tragedy is still ongoing.

Coast guard spokesman Nikos Alexiou told CNN over the phone last week: "When the boat capsized, we were not even next to (the) boat. How could we be towing it?" Instead, he insisted they had only been "observing at a close distance" and that "a shift in weight probably caused by panic" had caused the boat to tip.

The Hellenic Coast Guard has declined to answer CNN's specific requests for response to the survivor testimonies.

Direct accounts from those who survived the wreck have been limited, due to their concerns about speaking out and the media having little access to the survivors. CNN interviewed Rami and Mostafa outside the Malakasa migrant camp near Athens, where journalists are not permitted entry.

The Syrian men said the conditions on board the migrant boat deteriorated fast in the more than five days after it set off from Tobruk, Libya, in route to Italy. They had run out of water and had resorted to drinking from storage bottles that people had urinated in.

"People were dying. People were fainting. We used a rope to dip clothes into the sea and use that to squeeze water on people who had lost consciousness," Rami said.

CNN's analysis of marine traffic data, combined with information from NGOs, merchant vessels and the European Union border patrol agency, Frontex, suggests that Greek authorities were aware of the distressed vessel for at least 13 hours before it eventually sank early on June 14.

The Greek coast guard has maintained that people onboard the trawler had refused rescue and insisted they wanted to continue their journey to Italy. But survivors, relatives and activists say they had asked for help multiple times.

Earlier in the day, other ships tried to help the trawler. Directed by the Greek coast guard, two merchant vessels -- Lucky Sailor and Faithful Warrior -- approached the boat between 6 and 9 p.m. on June 13 to offer supplies, according to marine traffic data and the logs of those ships. But according to survivors this only caused more havoc onboard.

"Fights broke out over food and water, people were screaming and shouting," Mostafa said. "If it wasn't for people trying to calm the situation down, the boat was on the verge of sinking several times."

By early evening, six people had already died onboard, according to an audio recording reviewed by CNN from Italian activist Nawal Soufi, who took a distress call from the migrant boat at around 7 p.m. Soufi's communication with the vessel also corroborated Mostafa's account that people moved from one side of the boat to the other after water bottles were passed from the cargo ships, causing it to sway dangerously.

The haunting final words sent from the migrant boat came just minutes before it capsized. According to a timeline published by NGO Alarm Phone they received a call, at around 1:45 a.m., with the words "Hello my friend... The ship you send is..." Then the call cuts out.

The coast guard says the vessel began to sink at around 2 a.m.

The next known activity in the area, according to marine traffic data, was the arrival of a cluster of vessels starting around 3 a.m. The Mayan Queen superyacht was the first on the scene for what soon became a mass rescue operation.

A responsibility to rescue

Human rights groups say the authorities had a duty to act to save lives, regardless of what people on board were saying to the coast guard before the migrant boat capsized.

"The boat was overcrowded, was unseaworthy and should have been rescued and people taken to safety, that's quite clear," UNHCR Special Envoy for the Central Mediterranean Vincent Cochetel told CNN in an interview. "There was a responsibility for the Greek authorities to coordinate a rescue to bring those people safely to land."

Cochetel also pointed to a growing trend by countries, including Greece, to assist migrant boats in leaving their waters. "That's a practice we've seen in recent months. Some coastal states provide food, provide water, sometimes life jackets, sometimes even fuel to allow such boats to continue to only one destination: Italy. And that's not fair, Italy cannot cope with that responsibility alone."

Survivors who say the coast guard tried to tow their boat say they don't know what the aim was.

There have been multiple documented examples in recent years of Greek patrol boats engaging in so-called "pushbacks" of migrant vessels from Greek waters in recent years, including in a CNN investigation in 2020.

"It looks like what the Greeks have been doing since March 2020 as a matter of policy, which is pushbacks and trying to tow a boat to another country's water in order to avoid the legal responsibility to rescue," Omer Shatz, legal director of NGO Front-LEX, told CNN. "Because rescue means disembarkation and disembarkation means processing of asylum requests."

Pushbacks are state measures aimed at forcing refugees and migrants out of their territory, while impeding access to legal and procedural frameworks, according to the Berlin-based European Center for Constitutional and Human Rights (ECCHR). They are a violation of international law, as well as European regulations.

And such measures do not appear to have deterred human traffickers whose businesses prey on vulnerable and desperate migrants.

In an interview with CNN last month, then Greek Prime Minister Kyriakos Mitsotakis denied that his country engaged in intentional pushbacks and described them as a "completely unacceptable practice." Mitsotakis is widely expected to win a second term in office in Sunday's election, after failing to get an outright majority in a vote last month.

A series of Greek governments have been criticized for their handling of migration policy, including conditions in migrant camps, particularly following the 2015-16 refugee crisis, when more than 1 million people entered Europe through the country.

For those who lived through last week's sinking, the harrowing experience will never be forgotten.

Mostafa and Rami both say they wish they had never made the journey, despite the fact they are now in Europe and are able to claim asylum.

Most of all, Mostafa says, he wishes the Greek coast guard had never approached their boat: "If they had left us be, we wouldn't have drowned."