There have been acts of desperation in the port of Catania in Sicily, where rescue vessels have been docked with hundreds of migrants aboard.
On Monday, three men leapt into the harbor water from one of the vessels in an apparent bid to get to shore.
AFP news agency reported Doctors Without Borders (MSF) as saying that the men were quickly pulled to safety after jumping from the Geo Barents — a humanitarian vessel that rescues people in distress in the Mediterranean.
The MSF spokesman said that one of the three men who jumped had been attempting to save the other two.
A journalist with AFP reported that shortly after the men jumped, other migrants stood on the deck of the ship chanting, "Help Us!"
Migrants' stress 'very high' — MSF
The Geo Barents docked in Catania on Sunday, with Italian authorities allowing 357 people to disembark, among them children, while 215 others were forced to remain onboard.
"The ship has its limitations in terms of medical assistance, a ship is like an ambulance and people are still in the ambulance," Riccardo Gatti, head of search and rescue at MSF told AFP.
Gatti said that many on board were suffering from "infectious dermatological diseases" and that "their levels of psychological stress is very, very high."
A similar situation faces another humanitarian rescue vessel — the German-flagged Humanity 1 — which is docked nearby.
On Sunday 144 people were allowed to leave the ship, while 35 men considered to be healthy were refused permission to disembark.
It's reported that some onboard the Humanity 1 have embarked on a hunger strike.
Another migrant rescue ship called Rise Above, operated by German humanitarian group — Mission Lifeline — said that Italian authorities had directed its vessel with 89 on board to make its way to the port of Reggio Calabria.
"We are relieved that waiting on the high seas is over. The situation on board has become more and more critical in the past few
days and hours," Mission Lifeline spokeswoman Hermine Poschmann said.
Italy urged to follow international law
Italy wants the ships to move on to a new port, but the rescuers contend that according to international law they must be allowed to take those they pick up to the closest port of safety.
Italy's new right-wing government has vowed to stop the tens of thousands of migrants arriving on Italian shores each year.
The UN Refugee Agency (UNHCR) issued a statement appealing for all those onboard the blocked vessels to be allowed to disembark.
"Those stranded need to be disembarked swiftly without any further delay. We call on states in the region to protect the lives of those rescued by ending the current impasse and offering a place of safety for disembarkation," the UNHCR said.
The European Commission highlighted the need to ensure international laws were being observed.
"In line with international norms, every effort should be made to ensure that the time is minimized for the people remaining on board of these ships ... we encourage all relevant authorities to cooperate with each other in providing a suitable place of safety for the people on board in order to ensure the disembarkation."
Human rights watchdog Amnesty International also called on Italy to act in accordance with international law, saying "the law of the sea is clear; a rescue ends when all those rescued are disembarked in a place of safety."
kb/wd (AFP, dpa)