Europe's paramount human rights body, the Council of Europe, has called for an inquiry into the deaths of 61 migrants in the Mediterranean, claiming an apparent failure of military units to rescue them marked a "dark day" for the continent.

Mevlüt Çavusoglu, president of the council's parliamentary assembly, demanded an "immediate and comprehensive inquiry" into the fate of the migrants' boat which ran into trouble in late March en route to the Italian island of Lampedusa.

Yesterday, the Guardian reported that the boat encountered a number of European military units including a helicopter and an aircraft carrier after losing fuel and drifting, but no rescue attempt was made and most of the 72 people on board eventually died of thirst and hunger.

"If this grave accusation is true – that, despite the alarm being raised, and despite the fact that this boat, fleeing Libya, had been located by armed forces operating in the Mediterranean, no attempt was made to rescue the 72 passengers aboard, then it is a dark day for Europe as a whole," Çavusoglu declared. "I call for an immediate and comprehensive inquiry into the circumstances of the deaths of the 61 people who perished, including babies, children and women who – one by one – died of starvation and thirst while Europe looked on," he added.

Çavusoglu's intervention came as news emerged of another migrant boat which sank last Friday, according to the UN's refugee agency. Up to 600 were on board the overcrowded vessel as it fled the Libyan capital, Tripoli.

Witnesses who left on another boat shortly afterwards reported seeing remnants of the ship and the bodies of passengers in the sea. The International Organisation for Migration, which has staff on Lampedusa, said it had spoken to a Somali woman who lost her four-month-old baby in the tragedy, and said that it was unclear how many passengers had managed to swim to safety.

According to testimony collected by UNHCR workers in Lampedusa, migrants on the second boat setting sail from Tripoli attempted to disembark when they saw the first boat sink, but were prevented from doing so by armed men.

The UNHCR has insisted that more communication is needed between coastguards, military and commercial ships to minimise migrant deaths at sea.

"We need to take heed of a situation that is very much evolving. We have to cooperate much more closely," said a spokesperson, Laura Boldrini, adding that ships should not wait for a problem to arise before attempting to help migrant boats. "Rescue should be automatic, without waiting for the boat to break apart or the engine to stop running," she said.

Following the Guardian report into the plight of the migrant boat left to drift in the Mediterranean after suffering mechanical problems, Nato rejected suggestions that any of its units were involved in apparently ignoring the vessel. Officials pointed out that the Charles De Gaulle, a French aircraft carrier identified as having possibly encountered the boat, was not under direct Nato command at the time – although it was involved in the Nato-led operations in Libya.

"Nato vessels are fully aware of their responsibilities with regard to international maritime law regarding safety of life at sea," said a spokesman.

French defence officials denied that any of their ships were involved. "The [Charles De Gaulle] was never less than 200km (160 miles) from the Libyan coast," read a statement. "It is therefore not possible that it could have crossed the path of this drifting vessel which came from the Misrata region. If this was the case, it would have obviously come to the rescue of these people, in some way or another."

In 2010, the statement added, French naval vessels intercepted around 40 refugee boats and came to the assistance of more than 800 people.

Campaigners believe that calls for European ships to be more active in assisting migrants are now becoming more urgent. "All of these migrant boats are incredibly overcrowded and these are desperate people," said Professor Niels Frenzen, a refugee law specialist at the University of Southern California. "Given the hundreds of deaths we know about – and many more we probably aren't aware of – any migrant boat that's being observed right now is by definition a vessel that is in distress, and one which needs rescue."

Frenzen added that with Nato, the EU border agency Frontex, national coastguards and other unilateral forces all operating simultaneously in the Mediterranean, there was an "incredible mess of overlapping missions and jurisdictional confusion over the boundaries of different search and rescue regions".

"We've got this incredible concentration of ships and aircraft in that sea, many of which are there under security council resolution 1973 [which authorises military operations in Libya], the primary purpose of which is to protect civilian life," he said.

The UN refugee agency issued a warning for all vessels to keep an eye out for unseaworthy migrant boats in the Mediterranean.