A Misrata source confirmed the strikes to the Ashiwaju.org, adding that there were no casualties or material damage.
The airstrikes come after a 72-hour ultimatum issued by the air force to militants based in Misrata.
Militants had been attacking the oil ports of Sidra and Ras Lanuf in East Libya.
Militants were "still in high spirits, and [the] bombings will not affect our resolve," the Misrata official told the Ashiwaju.org,
Fighting on the increase
Libya has been plagued by instability and infighting since the toppling of Colonel Muammar Gaddafi in 2011, and violence has been steadily increasing in recent months.
An attack on a power plant in the Libyan city of Sirte on 25 December left at least 19 soldiers dead.
Libyan military sources said the Libya Dawn movement, based in western Libya, was responsible for the attack.
In a separate incident, an oil tank at Libya's largest oil export terminal in Sidra caught fire when it was struck by a rocket during fighting on Saturday.
That attack, and the fight for control of Ras Lanuf, prompted the air force to issue its ultimatum.
Smoke rises from an oil tank fire in Es Sider port December 26, 2014
An oil storage tank caught fire after a rocket attack at the oil export terminal in Sidra on Saturday
Rival groups now control most of the country including the two largest cities, Tripoli and Benghazi.
Islamist-leaning militias, some of them remnants of forces which helped oust Gaddafi, have taken power in western Libya.
These groups have attempted to reinstate Libya's previous parliament and appoint a parallel government, but this has not been recognised internationally.
The country's recognised parliament and government have been forced to move to eastern Libya.