Those rescued claimed five different ships did not offer them assistance
The medical charity Médecins Sans Frontières (MSF) says 141 people have been rescued from the Central Mediterranean.
The search and rescue vessel Aquarius, chartered by SOS Mediterranee, responded on Friday.
The ship rescued 25 people found adrift on a small wooden boat with no engine on-board.
It is believed they had been at sea for nearly 35 hours.
Later on Friday, the Aquarius spotted a second, overcrowded wooden boat with 116 people onboard.
Sixty-seven unaccompanied minors were among those on-board this vessel.
MSF says more than 70% of those rescued came from Somalia and Eritrea.
Many reported that they were held in inhumane conditions in Libya.
The people on board told rescue teams that they encountered five different ships which did not offer them assistance before they were rescued by the Aquarius.
Nick Romaniuk is search and rescue coordinator for SOS Mediterranee.
He says: "We are now following the instructions of the JRCC (Libyan Joint Rescue Coordination Centre) and will duly contact other RCCs for a place of safety to disembark the rescued people we have on board.
"What is of utmost importance is that the survivors are brought to a place of safety without delay, where their basic needs can be met and where they can be protected from abuse."
The organisations are calling on European governments to assign the closest place of safety, in accordance with International Maritime Law.
Aloys Vimard, MSF's project coordinator on-board the Aquarius, says: "European governments have put all their efforts into propping up the Libyan JRCC, however Friday’s events show that they do not have the capacity to fully coordinate a rescue.
"A rescue is not complete until there is disembarkation in a place of safety.
"The Libyan JRCC clearly told us they would not provide this.
"Additionally they did not inform Aquarius of boats in distress which they were aware of, despite the fact we were in the vicinity and offered our assistance.
"It was extremely fortunate that we spotted these boats in distress ourselves."