The Italian navy located the wreck in early May lying 85 nautical miles north of the Libyan coast.
Investigators say pictures of the wreck show bodies lying nearby, on the bridge of the ship and inside the hull.
"When this boat capsized and sank, we committed ourselves to go and check if there really were as many bodies as the survivors said," Renzi said after talks with French Prime Minister Manuel Valls in the northern Italian town of Trento.
"I made this commitment and I would like to confirm it once again," Renzi said.
"We will bring this boat to the surface and we will give a grave to these men and to these women, to these sisters and these brothers."
"If there is anyone in Europe or in the world who thinks one's own conscience can be buried at a depth of 387 metres, France and Italy will go and tell them that this is not possible," Renzi said.
Just 28 survivors were rescued and taken to Italy and 24 bodies were picked up and buried in Malta. The survivors included a Tunisian and a Syrian who are suspected of being the captain of the trawler and his second-in-command.
The tragedy on the night of April 18th sparked calls for more to be done to tackle human trafficking by sea and to ease the pressure on frontline states like Italy, Greece and Malta by having other countries take in asylum seekers.
Despite the dangers, the migrants keep coming. The Italian coastguard said it had coordinated the rescue of about 4,200 migrants trying to cross the Mediterranean on Friday, but also found 17 corpses on several of the rickety boats.