Libya is caught up in a conflict between that government and a second, internationally recognized one in the east, and the shooting comes as the United Nations pursues fragile negotiations between them to form a unity administration.
Hardliners on both sides are resisting a peace deal and see any violence as an excuse to challenge the talks.
Colonel Mustafa Al-Sharkasi, spokesman for the Tripoli government's chief of staff, said Tuesday the helicopter had been returning to the capital when it was hit by anti-aircraft fire and crashed into the sea near al-Maya, according to Reuters.
Security sources said 13 bodies had been recovered out of the 19 people on board, including three colonels from the Tripoli military command. They had been travelling by helicopter because of security risks on the coast road west of the city, a source said.
Fierce clashes erupted immediately after the crash between armed brigades from Zawiya city, which support the Tripoli government, and from Washafana town, whose fighters it blamed for shooting down the helicopter. No group claimed responsibility for the attack.
Four years after the revolt that toppled Muammar Gaddafi, Libya still has no national army. Brigades of rebels have been put on the state payroll as security forces. But they often remain more loyal to their cities or regions, and have steadily turned again against one another and allied with rival political forces in a battle for control.
"We firmly condemn the incident and of course, we accuse elements of the so-called tribal army of Gaddafi's followers. We will respond strongly at the right time and place," Sharkasi said in a statement, referring to the Washafana fighters.
The international community is pushing hard for factions to sign up to the UN agreement as a way to end a crisis analysts fear could fracture an already deeply divided country. In the chaos, Islamic State in Iraq and the Levant militants have gained ground and people smugglers are taking advantage to ship illegal migrants to Europe.