"We will go to the bottom of the sea and recover that boat," Matteo Renzi said in a television interview, as opposition mushroomed to controversial plans for quotas to spread Mediterranean refugees around Europe.
"There are 500 to 600 bodies down there. The world has to see what happened. I want those who are being cunning and pretending not to see, to stop," he said in a reference to EU partners refusing to help Italy deal with the waves of migrants washing up on its shores.
"Europe cannot just say 'out of sight, out of mind'".
Renzi said it would cost "between €15 to €20 million " to bring up the boat, which sank off Libya last month in the Mediterranean's worst disaster since World War II.
"I hope the European Union will pay, otherwise we will," he added.
There were over 700 people on board at the time, many of whom - including children - were packed in below deck, according to images filmed by a navy submersible.
The tragedy 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.
European Commission chief Jean-Claude Juncker unveiled a plan last week to make the rest of the 28-nation EU share the burden.
But France has made a dramatic U-turn since then, meaning that Brussels can no longer count on the support of the EU's second most powerful member after Germany.
President Francois Hollande said on Tuesday there was "no question" of migrant quotas in Europe, echoing comments by French Prime Minister Manuel Valls on Saturday.
Spain quickly followed suit and now 10 EU nations out of 28 say they oppose the quotas.