The GNA said in a statement that three separate rescue operations were carried out: 182 migrants were rescued in the first two operations and 87 others in the third held on the northeastern coast of Tripoli.
The statement said 84 of the rescued migrants were from Sudan but did not disclose the nationalities of the others.
Every year, thousands of irregular migrants use Libya as a gateway to cross the Mediterranean to Europe in overcrowded boats, often dying in the process.
Their numbers have declined since mid-2017 after Italy introduced a policy to return migrants to Libya if found at sea.
The policy has drawn condemnation from human rights activists as Libya has remained beset by turmoil since long-serving leader Muammar Gaddafi was ousted and killed in a bloody NATO-backed uprising in 2011.
Since then, the country has seen the emergence of two rival seats of power: one in eastern Libya, to which military commander Khalifa Haftar is affiliated, and another in Tripoli, which enjoys UN recognition.