At least 79 people are confirmed to have died in the disaster.
Rescuers saved 104 passengers from the boat that sank in deep waters off Greece’s coast early on Wednesday while trying to travel from Libya to Italy.
Authorities fear that hundreds of others –including women and children– may have been trapped below deck.
If confirmed, that would make the tragedy one of the worst ever recorded in the central Mediterranean.
The International Organization for Migration estimated that the vessel was carrying 700 to 750 people, including at least 40 children, based on interviews with survivors. Save the Children put that number higher, at about 100 children.
Greece is one of the main routes into the EU for refugees and migrants from the Middle East, Asia and Africa, Al Jazeera reported.
Under a conservative government in power until last month, Greece has taken a harder stance on migration, building walled camps and boosting border controls.
The United Nations has registered more than 20,000 deaths and disappearances in the central Mediterranean since 2014, making it the most dangerous migrant crossing in the world.