All parties represented in the Corsican assembly backed a motion proposed by Bonifacio mayor Jean-Charles Orsucci, a member of President Emmanuel Macron's Republic on the Move party, calling for the establishment of a committee of local and national representatives to organise the "efficient reception of migrants".
The assembly passed a similar motion in 2015 and local leaders offered to take in migrants aboard the Aquarius rescue ship when Italy and Malta refused to take them earlier this month.
On Monday the assembly's president, Jean-Guy Talamoni, said he was ready to help migrants picked up from another boat that had been refused entry by Italy.
The government representative on the island, Josiane Chevalier, declared that such a decision was the remit of the French state and not local authorities.
Macron says no migrant centres in France
A European Union summit this week proposed the establishment of reception centres but left it up to member states to decide whether they would open them.
While praising the deal as an example of "cooperation", President Emmanuel Macron declared that France will not open any because it is not a "first-arrival country".
Meanwhle, Italy, which hailed the deal as a recognition of its concerns as a first-arrival country, on Friday refused to allow a third NGO rescue boat to dock, even though it had no migrants aboard.
More than 650,000 migrants have landed in Italy since 2014, although the number has fallen drastically this year.
About 1,000 people have died trying to cross the Mediterranean so far this year, according to a UN estimate.
Babies' bodies washed ashore
The lifeless bodies of three babies were brought ashore in Libya on Friday, the latest identified victims of a Mediterranean migrant shipwreck from which survivors said 100 people are still missing.
The passengers included several Moroccan families, none of whom survived.
The only bodies recovered were those of the three babies, while the rest of the dead were left at the scene "for lack of resources" according to a Libyan coastguard employee.