The European Union’s official watchdog has opened an inquiry into the role of the bloc’s Frontex border agency in the shipwreck off Greece last month in which hundreds of people died.

Migrant crossings in unseaworthy boats organised by human traffickers from northern Africa have surged this year, with massive loss of life.

EU Ombudsman Emily O’Reilly wants her investigation to make clear to the public “who is accountable for these deaths” as Frontex has unclear jurisdiction and limits to its authority over member states like Greece when it comes to addressing the needs of those in distress at sea.

Key questions raised by the tragedy in the Mediterranean include to what extent Frontex could have been more involved in the rescue, what exactly did it communicate to the Greek authorities, and what level of responsibility, if any, the EU agency has for the shipwreck.

Ms O’Reilly said: “A tragedy of this magnitude requires all those involved to reflect on their responsibilities and to be clear to the public who is accountable for these deaths.”

As many as 750 people may have been on board the migrant ship that sank on June 14. So far, 82 bodies have been recovered and hundreds are still missing. Just over 100 survived.

Greece has been widely criticised for not trying to save the migrants before the sinking in international waters.

Officials in Athens say the passengers refused any help and insisted on proceeding to Italy, adding that it would have been too dangerous to try to evacuate hundreds of unwilling people from an overcrowded ship.

The ombudsman’s probe comes on top of Greek authorities looking into the responsibilities of their own coastguard in the tragedy.

Ms O’Reilly said: “It has been reported that in this instance Frontex alerted the Greek authorities to the ship’s presence and offered assistance but it is not clear what else it could or should have done.”

Any new analysis coming out of the investigation could help those adrift in the Mediterranean in the future, she added.