Three rescue boats run by civilian organisations have been waiting for more than a week off the coast of the EU countries hoping to dock and unload.
Despite several requests to Maltese authorities and Italian authorities, the Geo Barents, Ocean Viking and Humanity 1 vessels have yet to be assigned a port for disembarkation.
Meanwhile, the situation on board the ships is deteriorating, say the charities that run them.
The Doctors Without Borders (MSF) charity, whose Geo Barents vessel is carrying 572 rescued migrants, wrote on Twitter that there were three pregnant women and more than 60 minors on board.
SOS Humanity, which runs the Humanity 1, has 179 people on board its vessel, and the Ocean Viking, which is run by SOS Mediterranee, is currently carrying 234.
The NGOs say some of those rescued need urgent assistance. The charities say that all their requests to dock have proved unsuccessful thus far and criticised the coastal states’ “blatant” inaction.
Deputy search and rescue leader for MSF, Ricardo Gatti, singled out Malta for “failing to arrange or provide a place of safety to disembark.”
Meanwhile, the Italian interior minister Matteo Piantedosi told the Corriere della Sera daily newspaper on Wednesday that Italy “cannot take in migrants who are picked up at sea by foreign ships operating without any planned co-ordination with the authorities.”
While Mr Piantedosi did not say if and when the rescue boats would be allowed to dock he said that Italy would “never waive its duties to rescue people at sea, but we believe the time has come for European solidarity to finally become concrete.”
The minister said that people rescued by the three NGOs whose ships are currently stranded at sea account for 16 per cent of migrant arrivals in Italy and that Italian coast guards had rescued the remaining 84 per cent.
Italy’s new Prime Minister Georgia Meloni has suggested that the countries under whose flags the ships are operating should take in the rescued migrants.
The Humanity 1 sails under the German flag, while the other two vessels operate under the Norwegian flag.
She said the alternative was that her government might ban the ships entering Italy’s waters altogether.
“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,” said Ms Meloni.
The far-right leader has regularly called for a “naval blockade” at sea to prevent “illegal departures” to Italy.
According to the latest figures from the UN refugee agency, there have been just over 83,000 sea arrivals to Italy this year.