French Interior Minister Gerald Darmanin said Italy would not bear "the burden of this arrival alone".
France and Germany have called on Italy to grant a safe port to a humanitarian rescue ship carrying nearly 1,000 migrants.
French Interior Minister Gérald Darmanin said has no doubt that Italy will "respect international law" and welcome the Ocean Viking vessel.
The Norway-flagged ship has been stuck at sea for two weeks with 234 migrants recently rescued by the European NGO, SOS Méditerranée.
Humanitarian groups have called on Italy's new right-wing government to help the migrants disembark amid fears of worsening weather conditions and a shortage of provisions on board.
But Italy's Interior Minister Matteo Piantedosi has issued a directive warning that he was considering banning humanitarian ships from Italian ports.
Piantedosi has drafted new measures, claiming that the NGOs have violated procedures by not properly coordinating their rescues. The move is similar to previous anti-NGO policies under former Interior Minister Matteo Salvini.
In response, Darmanin told BFM TV on Friday that Italy would not bear "the burden of this arrival alone".
"We have told our Italian friends, along with our German friends, that we are ready to take some of the women and children, as we have done previously."
The German Foreign Ministry has asked Italy to intervene quickly to help 179 people on board the German-flagged Humanitarian 1.
Also at sea is the Norwegian-flagged Geo Barents, run by Doctors Without Borders (MSF), with 572 people on board.
The humanitarian groups say it is their duty to rescue people in distress at sea and have denied violating procedures.
Meanwhile, Italian authorities continue to allow arrivals of more than 6,000 people rescued by Italian patrols in the last week, including 456 who arrived in Calabria on Thursday.
Migrant arrivals by sea to Italy have risen to 85,991 this year, compared to 53,825 in the same period in 2021.
The UN refugee agency says that coastal states are obligated to accept people from rescue ships “as soon as practicable” and that governments should cooperate to provide a place of safety for survivors.
European Commission spokeswoman Anitta Hipper said the commission is aware of the three ships seeking safe disembarkation but has emphasised that it does not coordinate operations at sea or landings.
“Saving lives at sea is a moral duty as well as a legal obligation for member states under international law, independently from circumstances which have led people to the distress at sea,” Hipper told reporters.