The latest attacks were aimed at military positions in the capital's southern Al-Sabaa district, said Mohamed Younes, a spokesman for the Tripoli-based government.
For more than 40 years, Moammar Gadhafi was the eccentric strongman in power in Libya.
"Today on the Martyrs Square, we support the heroes of our armed forces taking part in the military operations against the invasion of gangs led by the terrorist Khalifa Haftar's". He said he supported Haftar's "role in counterterroism" and that Washington needed Haftar's "support in building democratic stability there in the region".
The White House says President Trump has spoken to Gen Haftar, suggesting the U.S. may also endorse a new government under his command.
The statement made no mention of Haftar's offensive on Tripoli, and Trump's praise for the rogue Libyan general signals a departure from previous administration statements condemning Haftar's march on the capital.
Jalel Harchaoui, research fellow at the Clingendael Institute worldwide relations think tank in The Hague, said the Trump phone call was tantamount to supporting Haftar's operation and thus is "creating an environment where a military intervention by foreign states, like Egypt, is likelier". Both countries flew airstrikes on Tripoli in 2014 during a different conflict to help a Haftar-allied force, US officials said at the time. Tunis is officially neutral in the Libyan conflict and has hosted repeated diplomatic negotiations on Libya's future.
Asked whether that included ruling the whole country, the official said, "That is up to the people of Libya".
We're joined by Anas El Gomati, director of the think tank The Sadeq Institute.
Several airstrikes and explosions shook Tripoli overnight in an escalation of an assault on the Libyan capital by the warlord Khalifa Haftar.
"We condemn the criminal acts against the Libyan people and the support for the rebel Haftar".
Russian Federation said it was not helping Haftar's forces and it supported a negotiated political settlement that ruled out any new bloodshed.
France dismissed the allegation even after it recently moved to prevent the European Union (EU) from condemning Haftar's push into Tripoli.
Since then, the country has seen the emergence of two rival seats of power: one in eastern Libya, to which Haftar is affiliated, and another in Tripoli, which enjoys United Nations recognition.
Government forces announced the launch of a "new phase" in the battle for Tripoli with a counter-offensive against Haftar forces.
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