"For the moment it's 'no'," Le Maire said in an interview to French broadcaster BFMTV when asked if Paris was ready to respond positively to a request from charities for permission to dock with 58 migrants aboard in Marseille.
The French minister argued that ships were supposed to get docking access at the nearest port under European rules and Marseille was not the nearest one.
The migrant rescue ship -- run by SOS Mediterranee and Doctors without Borders (MSF) -- has been turned away by Italy and forced to stop in Malta and Spain in recent months.
Meanwhile, French Minister for European Affairs Nathalie Loiseau, said on Tuesday that she hoped the EU finds a solution during the day.
"Since yesterday the ministers of the interior of the European Union ... are working non-stop, I hope we have an answer within the day," Loiseau told French radio Sud Radio.
"We will find a solution," she said, recalling that other similar crises had been solved in recent months by an agreement to share the acknowledgement of migrants between several EU countries.
France's government spokesman Benjamin Griveaux, tweeted on Monday that the solution will come from "cooperation with our European partners."