The latest sinking happened off the shores of Garabulli, a town some 60km east of the Libyan capital, Tripoli.
The rescue operation was reportedly carried out by the "Ibn Auf" vessel.
Patrols had found 31 bodies and 60 survivors from one boat, along with a further 140 survivors from a second.
"When we arrived at the spot, we found an inflatable dinghy with several people clinging to part of it", said coastguard spokesman Colonel Abu Ajila Abdelbarri. Some of the people drowned after the boat sank included children.
"We looked for other survivors for more than five hours", he said.
About 250 people were rescued by the Libyan coastguard on Thursday.
"We were able to rescue one woman after we heard her shouts", he said.
Those rescued by Libya's coastguard on Saturday were brought back to a naval base in Tripoli where the authorities provided them with water, food and medical care.
After record arrivals from 2014 to 2016, the European Union's deal with Turkey to stop arrivals to Greece and blocks on migrants inside Libya and off its coast have greatly reduced the flow, the International Organization for Migration (IOM) said.
A total of 35 others were rescued, Qasim added.
They had been trying to cross the Mediterranean along with another boat.
The Mediterranean Sea remains "by far the world's deadliest border", according to a United Nations study published on Friday by the International Organization for Migration (IOM).
Footage broadcast by CNN appear to show African migrants being traded in Libya sparked an worldwide outcry and protests in Europe and Africa.
Libya's United Nations -backed government said on Thursday it was investigating reports of African migrants being sold as slaves and promised to bring the perpetrators to justice.
People-trafficking networks have flourished in the chaos that followed a NATO-backed uprising which toppled long-time dictator Moamer Kadhafi in 2011.
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