Several migrants jumped into the sea from a Spanish rescue boat in a bid to reach shore in Italy.
Crew members, however, jumped in and brought them back aboard.
"Nine people have thrown themselves into the water trying desperately to reach the coast of Lampedusa," the ship Open Arms tweeted. "The situation is out of control."
Open Arms, with almost 100 migrants onboard, has been left stranded just off the port of Lampedusa after Italy denied permission from entering its waters.
Earlier, Italy's hard-line interior minister, Matteo Salvini, banned private rescue ships, saying they have become "taxis" for people smugglers.
“If the worst happens, Europe and Salvini will be responsible,” the charity said in a tweet.
Cardinals are scheduled to meet on Tuesday to plan Pope Francis' funeral, which leaders from around the world will attend ahead of a conclave next month to elect a new head of the Roman Catholic Church.
Russian President Vladimir Putin proposed on Monday bilateral talks with Ukraine for the first time since the early days of the war, and his Ukrainian counterpart Volodymyr Zelenskyy said Kyiv was eager to discuss a halt to attacks on civilian targets.
Ukraine issued air raid alerts for Kyiv and the country's eastern half as blasts shook the city of Mykolaiv early on Monday, authorities said, hours after the one-day Easter ceasefire declared by Russian President Vladimir Putin came to an end.
US Vice President JD Vance began a four-day visit to India on Monday and will hold talks with Prime Minister Narendra Modi, as New Delhi rushes to avoid steep US tariffs with an early trade deal and boost ties with the Trump administration.