Mr Talamoni, assembly chief from the French territory Corsica, told the French news channel BFMTV: “Europe has failed on migration.
“European states must now wake up and share responsibility for migrants rescued at sea.
“For years, we turned a blind eye to Italy’s migration problem and pretended it was Rome’s problem alone.
“But it has always been a problem for the whole of Europe.”
Mr Talamoni then called for a more fair distribution of migrants in the EU.
The Corsican lawmaker was commenting on the plight of the Aquarius rescue ship, which is stranded for the second time in the Mediterranean carrying 141 people after it was refused entry by Italy and Malta, the two countries closest to its current location.
The Aquarius, which was left stranded with more than 600 people on board in June after being denied safe harbour by Rome and Valletta, resumed operations off the Libyan coast last week.
The 141 migrants were rescued in two separate operations on Friday and are in a stable condition, the French charity that operates the boat, SOS Mediterranee, said.
“If the closest ports are closed, then others must be opened,” Mr Talamoni said, adding that Corsica would let the ship dock at of its ports if the French government gave it the all clear.
The director of the southern French port of Sète, Jean-Claude Gayssot, also said he would be prepared to let the Aquarius dock there.
But French President Emmanuel Macron’s office later told the AFP news agency that French ports were not the closest to the ship and therefore not the safest, before condemning Italy’s “very tough political stance” on migrants rescued at sea.
The Elysée Palace said that France was in touch with other EU countries to “rapidly” find a port where the Aquarius could dock.
Italy’s new policy of turning back humanitarian boats sparked a heated row among EU nations in June, which was only resolved when Spain’s new socialist government agreed to let the Aquarius dock at its southern port of Valencia.
Italy’s far-right interior minister Matteo Salvini has repeatedly refused entry to rescue ships run by foreign NGOs, which he has accused of colluding with people smugglers.
On Saturday, Mr Salvini said the Aquarius would “never see an Italian port again,” accusing it of encouraging migrants to risk the perilous journey to Italy in the knowledge that they will be rescued.