The migrants set off Friday from Sabratha -- a town 70 kilometers (45 miles) west of Libya's capital that has become a staging ground for traffickers -- but their boat's engine failed, a coastguard official said.
An AFP photographer at the scene of the rescue said the vessel was intercepted by a coastguard patrol boat around 20 nautical miles northeast of Tripoli.
The official said those on board were of various African nationalities and included 10 women and five children, including a baby.
Libya said Saturday it had intercepted more than 400 migrants bound for Europe in recent days.
The announcement followed a meeting of European Union leaders in Malta where they agreed moves to curb mass migration from Libya.
The plan includes funding and training Libya's coastguard to make it better able to intercept migrant boats and helping neighboring countries to close routes into Libya, according to a draft statement seen by AFP.
Lawlessness in Libya since a 2011 uprising that ousted longtime strongman Moammer Gadhafi has allowed smuggling networks to develop a lucrative trafficking trade.
Italy's coastguard said Thursday that more than 1,750 migrants had been rescued in the Mediterranean within 24 hours.
Around 230 people have died en route to Europe since the start of 2017, according to the United Nations.