The German-flagged MV Louise Michel said it was stranded and needed urgent help after lending assistance to a boat that was carrying at least one dead migrant.
The 31-metre (101-foot) vessel's crew said it was overcrowded and unable to move after encountering another boat attempting to cross the expanse of sea dividing Europe and Africa with 130 people on board.
"There is already one dead person on the boat. We need immediate assistance," the Louise Michel crew wrote on Twitter, saying other migrants had fuel burns and had been at sea for days.
An Italian coastguard patrol boat was launched from Lampedusa island and took on board the migrants most in need of aid, many of them women and children.
"In view of the danger the situation posed, the coastguards sent a patrol boat from Lampedusa... which took on board the 49 people in the most fragile condition - 32 women, 13 children and four men," the coastguard said in a statement.
Banksy artwork
The vessel's crew of 10 had earlier rescued another 89 people from a rubber boat in distress on Thursday.
They said on Twitter that there were a total 219 people on board and that they had requested assistance from the Italian and Maltese authorities.
The boat - named after 19th-century French anarchist Louise Michel - was around 90 kilometres (55 miles) southeast of Lampedusa on Saturday, according to the global ship tracking website Marine Traffic.
Thousands of people are thought to have died making the dangerous trip across the Mediterranean to flee conflict, repression and poverty in Africa and the Middle East.
Sea-Watch 4, which has rescued 201 migrants and is itself in search of a host port, also decided to help the Louise Michel "in the face of the lack of reaction" from the authorities, a spokesman for the German NGO Sea-Watch, which charters the boat with Doctors Without Borders (MSF), told AFP.
The Italian left-wing collective Mediterranea, meanwhile, announced it would send the ship Mare Ionio from the port of Augusta in Sicily to assist.
Banksy's decision to fund the high-speed boat follows a body of work by the artist that has levelled scathing judgements on Europe's halting response to the migrant crisis.
Painted in hot pink and white, the Louise Michel features a Banksy artwork depicting a girl in a life vest holding a heart-shaped safety buoy.
'An anti-fascist fight'
The motor yacht, formerly owned by French customs, is smaller but considerably faster than other charity rescue vessels - enabling it to outrun Libyan coastguard boats, according to The Guardian.
Its crew is "made up of European activists with long experience in search and rescue operations" and is captained by German human rights activist Pia Klemp, who has also captained other such rescue vessels, the paper reported.
Banksy's involvement in the rescue mission goes back to September 2019 when he sent Klemp an email asking how he could contribute.
Klemp, who initially thought it was a joke, told the paper she believed she was chosen because of her political stance, The Guardian said.
"I don't see sea rescue as a humanitarian action, but as part of an anti-fascist fight," she told the paper.
Early this month, humanitarian organisations said they would resume migrant rescues in the Mediterranean Sea, where none have operated since the Ocean Viking docked in Italy in early July.
Before the Ocean Viking's last mission, rescue operations in the Mediterranean had been suspended for months due to the global coronavirus pandemic.
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