Two migrant mothers and their two children on board the German rescue ship Sea-Eye have refused to leave without their fathers, Italian officials and the NGO said Friday.

"The women and children refuse to leave the ship. We can only wish them a good trip towards Berlin," Interior Minister Matteo Salvini said in a statement.

On Wednesday, the German-flagged ship rescued 64 people from an inflatable raft after efforts to contact the Libyan coastguard failed.

It headed for the Italian island of Lampedusa and on Friday an agreement was reached under which two children aboard, aged one and six, would be allowed to land with their two mothers and a pregnant woman.

The fathers were not allowed to accompany them however.

"To separate mothers and children from their fathers without a proper reason is active family separation and emotional torture," a Sea-Eye statement said.

In Berlin, an interior ministry spokesman told AFP the country was "ready to do its part" and welcome some of the 64 migrants within the framework of a European burden-sharing deal.

According to Sea-Eye, 47 German cities have offered to host the migrants, and it said that reserves of fresh water and food will soon run out owing to the large number of people on board.

Salvini, a leader of the far-right League party, reiterated last month that he would close Italian ports to migrant rescue NGOs operating in the Mediterranean, to force Europe to take its share of asylum seekers.

He said Thursday that his stance had been backed by fellow G7 interior ministers.

"The NGOs are a problem and they help human traffickers," Salvini charged.