The UN Refugee Agency says almost 400 refugees and migrants rescued by three ships in the Mediterranean must be allowed to disembark safely.
A joint statement issued with the International Organization for Migration said it was a “humanitarian imperative to save lives”.
Italy’s coastguard evacuated 49 people from an overloaded rescue vessel funded by British artist Banksy.
Another rescue boat SeaWatch 4 later took the remaining 150 on board.
The crew of the Louise Michel had earlier tweeted a call for immediate assistance. European authorities had not responded adequately, they said. Sea Watch 4 said late on Saturday it was now carrying 350 people who needed to disembark as soon as possible.
Chris Grodotzki, part of the Sea Watch 4 rescue team, told the BBC the people it picked up were “sea sick, they showed signs of fuel burns, they were disorientated, dehydrated”.
He said the situation on board was currently “stable” but that the vessel would not be able to carry that number of people for a long period of time.
“The decks are stuffed,” he said. “People are crammed together.”
A third boat also needs assistance. A group of 27 migrants and refugees, including a pregnant woman and children from Libya, have been aboard the Maersk Etienne since their rescue on 5 August.
The UNHCR and the IOM said the lack of a deal on a regional landing system could not be an excuse to deny vulnerable people safe harbour.
“It is essential that other EU member states provide more support to countries at the forefront of welcoming those arriving by sea in the Mediterranean,” the joint statement said.
The Louise Michel, a 31m boat which is funded by Banksy, has already carried out a number of rescue missions.
Its crew tweeted that they had managed to keep the vessel stable and had a dead body of a would-be migrant in its only life raft. Louise Michel and Sea Watch 4 say refugees and migrants have told them that at least two other people fell overboard before the rescue ship found the group, and were presumed dead.
The UNHCR then appealed for the urgent transfer of all those on board, warning that “any delays could jeopardise the safety of people on board, including the crew”.
On Saturday, the Louise Michel confirmed via Twitter that the Italian coastguard had taken 49 of the most vulnerable survivors but this left “the majority still waiting”.
The SeaWatch4 later tweeted it had taken the remainder of the Louise Michel’s migrants on board.
The Maersk Etienne said it had been asked by the Maltese authorities to rescue the 27 people on board in early August but had not been allowed to bring them ashore. The Maltese government says the migrants were rescued outside Maltese waters and the tanker had never been asked to sail to Malta.
“A commercial tanker cannot be considered a suitable place to hold people in need of humanitarian assistance or who may be in need of international protection,” the UNHCR and IOM said.
According to UN data, 443 people have died or have gone missing trying to cross the Mediterranean from north Africa so far in 2020.
Slightly more than 40,000 have arrived in Europe by sea during the same period.