Rescue ships and Libya's coastguard picked up several hundred migrants on Saturday.
Libyan coastguard vessels intercepted three migrant boats off Zawiya, just west of the capital, Tripoli.
One was an inflatable dinghy with 125 people on board.
The second boat was turned back off Garabulli, east of Tripoli, with 112 on board. The third, with 98 on board, was intercepted off Abu Kamesh near Libya's border with Tunisia.
One boat with more than 100 migrants on board made it as far as the Aquarius rescue ship about 21 miles from the coast to the west of Tripoli. The ship was preparing to transfer the migrants to Italy.
Rescuers on board the Aquarius said the migrant boat was on the verge of completely sinking when it reached them. More than half the migrants on it were Nigerians, The rest were from other sub-Saharan African countries as well as two Palestinians.
One of the Palestinians was thrown into the water by other migrants after trying to convince them that they would be better off being saved by a nearby Libyan coastguard boat than drowning, rescuers said.
Two other groups of migrants were transferred to the Aquarius late on Saturday. They included 62 who had been picked up by a merchant ship in offshore oil fields and 106 others from another charity vessel.
The coastguard in Zuwara, a former Libyan smuggling hub west of Zawiya, said they had foiled a departure during the night and arrested some migrants. Others reportedly escaped with smugglers.
Why is Libya the focus?
The country is the main departure point for migrants attempting to reach Europe by sea. More than 600,000 migrants have crossed the central Mediterranean to Italy over the past four years as people smugglers took advantage of a security vacuum in Libya.
Thousands more perished at sea.
Since last summer, the rate of departures dropped sharply after smugglers in the Libyan town of Sabratha struck a deal with the Tripoli government to halt their activities. They were then pushed from the town by rival armed groups.
Libya's EU-backed coastguard has also stepped up interceptions, often cutting migrant boats off before they can reach international vessels that would bring them to Europe.
What they are saying
"All but one of the five balloons holding the boat up was either completely deflated or deflating and there were still about 120 people inside the boat, so a very, very precarious condition," - Max Avis, rescuer.