The Migrant Offshore Aid Station (MOAS) said in a statement they "believe there have been deaths," but it is not clear how many people have drowned.
So far rescuers have pulled 453 people to safety, but were forced to suspend the operation overnight with their rescue vessel the Phoenix running at full capacity.
The charity's founder, Christopher Catrambone, said yesterday: "Nobody has ever seen anything like what we are witnessing this weekend."
He later described in a tweet carrying a dead child on board the ship at Easter.
"There were 8-10 people dead on board but the situation is not finished yet," said Michael Buschheuer, founder of Sea-Eye, another rescue charity based off the coast of north Africa.
"At the moment, many boats will not get found, they will get lost. Definitely, on our boat there were about 10 (drowned), but maybe there are 300, I have no idea. It is still ongoing."
"Around us are another 400 people -- many of them woman and children -- in small rubber boats and small wooden boats," Pauline Schmidt, a press officer with another charity Jugend Rettet who is on board the Iuventa rescue ship, said in an email to CNN.
"Not all of them wear life jackets. No vessel nearby that can provide help to us. Also around 5 more rubber boats coming northwards in our direction. We are not able to navigate anymore due to the high amount of persons on board."
Earlier this week the International Organization for Migration said nearly 32,000 migrants and refugees entered Europe by sea in 2017 through 9 April, with over 80% arriving in Italy and the rest in Spain and Greece. The organization said 554 drowned making the crossing.
As the rescue effort continued, bad weather was complicating matters further, MOAS said in a tweet. All three charities said that calls for help to the Maritime Rescue Co-ordination Center in Rome had not yet been answered.
Separately, Medicins Sans Frontieres and Italian authorities said they had successfully brought to shore 649 migrants in the southern Italian port of Reggio di Calabria.
Another boat carrying 72 migrants landed this morning at the nearby seaside resort of Melito Porto Salvo.
"There were Somalis, Afghans, Syrians and Bangladeshis on board. We will taken them first to be registered with the police and then they will be taken on buses to reception centers" said Francesco Campolo, senior officer with the Italian state police in Reggio di Calabria told CNN.
Some 6,000 migrants were rescued by the Italian coast guard on Friday and Saturday alone according to Italian newspapers -- as people smugglers in Libya took advantage of calm seas to launch boats.