ATHENS — Shortly after a rickety fishing boat carrying hundreds of smuggled migrants sank in front of a Greek Coast Guard vessel last week, Greek officials explained that they had not intervened because the smugglers didn’t want them to.

Intervening also would have been dangerous, Coast Guard spokesman Nikos Alexiou has said, given that the ship was overcrowded and filled with migrants intent on reaching Italy.

Trying to “violently stop its course” without cooperation from the crew or passengers could have provoked a “maritime accident,” Mr. Alexiou said. He added that even though the ship was in Greece’s search and rescue territory, “you can’t intervene in international waters against a boat that is not engaged in smuggling or some other crime.”

Mr. Alexiou apparently meant smuggling drugs or guns, not people. But in the aftermath of the deadliest shipwreck in Greece in a decade, and perhaps ever, with possibly more than 700 men, women and children from Syria, Pakistan and Egypt drowned, the decision not to intervene has raised concerns that an alignment of interests between smugglers paid to reach Italy and Greek authorities who would rather the migrants be Italy’s problem led to an avoidable catastrophe.

“If the Greek Coast Guard recognized the boat as in distress, and this is an objective assessment, they should have tried to rescue them no matter what,” said Markella Io Papadouli, a lawyer specializing in maritime law and human rights at the Advice on Individual Rights in Europe Centre. She said no SOS call had been required, as the Greeks have insisted. And while there were reports of distress calls being relayed to the Greeks, she said that focusing on the call was besides the point.

“Regardless of what the smugglers wanted,” or where the migrants hoped to go, she said, “you have an obligation to rescue” when a ship is in grave danger. “Negotiating with the smugglers is like negotiation with plane hijackers.”

On Monday, the Greek authorities came under more pressure as new accusations of negligence surfaced and survivor accounts began to trickle out, describing a hapless captain, engine trouble and even suggestions that the Greek Coast Guard had accidentally caused the sinking.

The Coast Guard disputed a BBC report demonstrating that the trawler full of migrants didn’t move for seven hours on Tuesday. The Greek Coast Guard on Monday countered that the boat had traveled 30 nautical miles from its detection Tuesday morning until it sank.

Greek officials are pointing the finger at the nine men currently under arrest. The suspected smugglers, they say, rejected water to keep migrants thirsty and docile and to maintain control.

But experts say the Greek authorities also violated maritime law. A 2014 European Union law “establishing rules for the surveillance of the external sea borders” counts among the criteria for rescue “the existence of a request for assistance, although such a request shall not be the sole factor for determining the existence of a distress situation.”

The other factors for a rescue read like a description of last week’s shipwreck. Among the criteria: “The seaworthiness of the vessel and the likelihood that the vessel will not reach its final destination,” “the number of persons on board in relation to the type and condition of the vessel,” and “the availability of necessary supplies such as fuel, water and food to reach a shore.”

They also include: “the presence of qualified crew and command of the vessel,” “the availability and capability of safety, navigation and communication equipment,” “the presence of persons on board in urgent need of medical assistance,” “the presence of deceased persons on board,” and “the presence of pregnant women or of children on board.”

As of Monday the authorities had recovered 81 bodies, and had transferred most of the 104 survivors from a hospital in Kalamata, a port in southwestern Greece, to a reception center north of Athens, where access is restricted.

In Pakistan on Monday, Prime Minister Shehbaz Sharif declared a day of mourning for the 104 Pakistanis already locally confirmed dead, though officials expect the toll to rise.

Many of the missing were from the Pakistani-administered part of Kashmir, the region long contested between India and Pakistan, and nearby in Punjab, Pakistan’s most populous province. Mr. Sharif said Sunday on Twitter that law-enforcement agencies had been asked “to tighten the noose around individuals involved in the heinous act of human smuggling.”

United Nations officials have called for an investigation into what went wrong at sea.

The shipwreck occurred during a caretaker government in Greece ahead of elections on Sunday, dulling the political impact. Still, Kyriakos Mitsotakis, projected by polls to win re-election as prime minister, and whose harsh line on migrants has proved popular at home and in the European Union, laid the blame entirely on the human traffickers.

“As stunned as we are, we should also be outraged at the wretched smugglers, at those scum,” he said while campaigning in Gytheio in the southern Peloponnese on Saturday.

But the account of the Greek government has shifted over recent days. At first, the Coast Guard denied having ever tied ropes onto the fishing boat, which some survivors claimed was the cause of the shipwreck. Then the Coast Guard acknowledged that it had tied one rope briefly to ascertain the condition of the boat and passengers, some of whom, survivors said, were already dead from exposure and thirst.

The Greeks have said they wanted to stabilize the boat while critics have expressed fears that the Greeks may have been trying to tow the migrants out of their jurisdiction.

A migrant advocacy group, Alarm Phone, said that as early as noon on Tuesday, it had received calls that the vessel was in distress and that it had relayed this information to the authorities. The Greeks say that in their communications with the vessel throughout the day they were told the ship intended to sail to Italy.

The BBC also reported that a merchant ship, the Lucky Sailor, had confirmed it diverted course after being asked by the Greek Coast Guard to give the trawler food and water. According to court documents obtained by The New York Times, another ship, the Faithful Warrior, arrived about two-and-a-half hours later, and at 9:30 p.m. provided passengers with food and water. Migrants could be heard chanting “Italia, Italia.”

At 9:45 p.m. the Faithful Warrior’s captain, Panagiotis Konstantinidis, reported to the Hellenic Search and Rescue Center control center that the trawler was “rocking dangerously” because of the overcrowding on the decks. A few minutes later passengers threw supplies into the sea.

According to the documents, an official on Coast Guard Vessel 920 reported the fishing boat as having stopped at 11:45 p.m., which is when, he said, the sailors threw it a rope.

“Voices were heard in English — ‘No help, Go Italy’— and despite repeated appeals asking them if they wanted help, they ignored us and at around 23:57 they released the rope. They started the boat’s engine again and moved in a westerly direction at low speed.”

According to Mr. Konstantinidis’s testimony, the control center dismissed his ship from its relief mission at 12:18 a.m. and instructed it to leave the area. A woman who answered the phone at the shipping firm that owns the Greek cargo ship Faithful Warrior said that the Coast Guard had told the firm not to comment and to direct inquiries to the Coast Guard.

“The Coast Guard still claims that during these hours the boat was on a course to Italy and not in need of rescue,” the BBC reported.

In the court documents, the Coast Guard official noted in neat and apparently uninterrupted handwriting on his deck log, that at 1:40 a.m. the ship stopped moving again and the Coast Guard approached to assess the situation and prepared for the possibility of a rescue. But 26 minutest later, at 2:06 a.m., he reported that the ship “had begun to take a great inclination to the right side, and there was great upheaval and screams.”

“Within a few seconds the vessel capsized, resulting in the people on the external deck to fall in the sea, and the vessel to sink.”

Jason Horowitz and Niki Kitsantonis reported from Athens, and Matina Stevis-Gridneff from Brussels. Gaia Pianigiani contributed reporting from Siena, Italy.