Three charity boats carrying almost 1,000 rescued migrants on Wednesday urged Italian or Maltese authorities to let them dock in one of their ports, saying those onboard needed urgent assistance.
Doctors Without Borders (MSF), SOS Mediterranee and SOS Humanity, who are operating the ships, have been at sea for more than a week.
They said all of their requests to dock have so far proved unsuccessful.
"Five hundred and seventy-two men, women and children still waiting for a safe port," MSF wrote on Twitter, referring to its Geo Barents vessel.
SOS Humanity told Reuters it had 179 people onboard its Humanity 1 vessel off the eastern coast of Sicily.
The German charity said it had been sending requests to dock to state authorities for the past 11 days.
The vessel run by SOS Mediterranee is carrying 234 people.
Italian Interior Minister Matteo Piantedosi did not reply to a question from the Corriere della Sera daily on whether the migrant boats would be allowed to dock.
But Mr Piantedosi said Rome could not take charge of migrants rescued at sea by "foreign boats".
Migrant children rescued in French waters - in pictures
There was no immediate response from Maltese authorities to a request for comment.
Italian Prime Minister Giorgia Meloni's new right-wing government is threatening to ban charity ships from its waters, as Rome looks again to embrace a tough stance against boat migrants.
In comments to be included in a book, confirmed by her staff, Ms Meloni accused sea-rescue charities of breaching international law by acting as a "shuttle" between Africa and Europe.
Dramatic clifftop rescue after migrants’ boat sinks in Greek waters - video
Dramatic clifftop rescue after migrants’ boat sinks in Greek waters
She said Germany and Norway, the flag nations of the charity ships in question, should take care of the migrants stranded at sea, rather than Italy or Malta.
"If an NGO ship flies, let's say, the flag of Germany, there are two possibilities: either Germany recognises it and takes care of it, or that ship becomes a pirate ship," Ms Meloni told book author Bruno Vespa.
