One of the ships had been given permission by Italy to disembark some migrants in need of assistance, while the other vessel reports that it has not been given permission to approach a port.
Currently, four European ships remain in the Mediterranean with 1,100 migrants on board and nowhere to land.
Some of the ships have been at sea for two weeks.
Meanwhile, Italy’s only black lawmaker in parliament, Abourbakar Soumahoro, has announced that he will join other African migrants on board the ships if the government of Italian Prime Minister Giorgia Meloni does not allow the ships into port.
In addition, Interior Minister Matteo Piantedosi announced that one of the ships will be allowed into an Italian port only long enough to disembark minors and others in need of medical care.
Responding to critics this week, Italy’s new government said the countries whose flag the charity-run rescue ships operate must disembark in their home ports.
“We stop being hostage to these foreign and private NGOs that organize the routes, traffic, transport and migration policy,” Infrastructure Minister Matteo Salvini, known for his anti-migrant stance as interior minister in 2018-19, said in an online post.