"If a boat had France as its closest coast, it could land," Griveaux said. "France has done its bit, but what is unacceptable is the behaviour and political instrumentalisation of the Italian government."
Successive Italian governments have accused their European partners of leaving the country to cope on its own with an influx of 700,000 migrants from Africa since 2013.
"You can't create a precedent that will enable one European country to offload onto other European countries," he continued. "We need to show solidarity which Italy has not shown."
The new Italian government has pledged to deport hundreds of thousands of people living in the country illegally and stop boats carrying migrants from landing on its shores.
Macron has faced criticism from some leftist opposition parties and members of his own Republic on the Move party for not offering to take in the 600 people on board the Aquarius.
Spain has offered to take them in, which Macron praised during the cabinet meeting.
A spokesman for Macron's Republic on the Move party earlier said the Italian government's policy was "sickening."
"The position, the line of the Italian government is sickening. It's unacceptable to play politics with human lives which is what is happening at the moment," Gabriel Attal told the Public Senat channel.
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