A ship with 42 rescued migrants onboard was anchored off Italy's southern-most island of Lampedusa for a second day on Thursday in the latest stand-off between Italy's hard-line interior minister and humanitarian groups.
Despite growing pressure from inside Italy and Europe, Interior Minister Matteo Salvini has refused to allow the migrants to set foot in Italy.
The EU Commission said member countries had stepped up to accept the migrants but a solution could only be worked out when the migrants were on land.
Meanwhile, small demonstrations in Italian cities including Rome, Milan and Palermo have expressed solidarity with the Sea-Watch crew and the migrants aboard.
Sea-Watch 3 captain Carola Rackete said in a video message on Thursday morning that she still had no clear indication of when the rescued passengers would be allowed on land.
Ms Rakete said she hoped a delegation of Italian parliamentarians expected to visit later in the day "will create the necessary momentum to finally disembark everyone and get them to a place of safety".
She repeated that she took the ship into Italian waters without permission out of necessity, because of the psychological state of the passengers and the worsening humanitarian conditions on board.
"I cannot guarantee the safety of the rescued people on board my vessel," Ms Rakete said.
Mr Salvini has threatened to seize the Dutch-flagged ship operated by the German group Sea-Watch, and to arrest the crew.
He said they breached the law by ignoring orders not to enter Italian waters, and a special government measure that specifically banned the Sea-Watch 3 from Italian jurisdiction.
In Brussels, the EU's top migration official has urged Italy to help take the 42 migrants to Lampedusa as soon as possible. He did not identify which countries are willing to take in the migrants.
"I hope that Italy, in this particular incident, will contribute to a swift resolution for the persons onboard," Migration Commissioner Dimitris Avramopoulos said.
Those on board are among 53 that the group said it rescued June 12 from a rubber boat off Libya in international waters.
Eleven were taken to Italy for medical reasons. The remaining 42 include a 12 year old and two other children travelling alone.
Sea-Watch said in a separate message that they could not wait another night at sea.
"Desperation of people in need is nothing to gamble with," the organisation said.
While Mr Salvini continues to focus on humanitarian rescue ships, which he accuses of aiding migrant traffickers by encouraging departures from Libya, arrivals of smaller migrant boats, mostly from nearby Tunisia, continue.
Ten migrants arrived in the port of Lampedusa early on Thursday, Ansa news agency reported.