Armed groups clashed in Tripoli, Libya's capital, on Friday night, local media reported.
Exchanges of heavy gunfire and explosions were heard across several districts of Tripoli, AFP reported.
Images broadcast by the local media showed civilians fleeing.
The fighting involved two militias from western Libya, local media reported.
No casualties or motive for the fighting were apparent. It is the latest violence to rock the country as two rival prime ministers vie for power.
After a 2011 revolt toppled dictator Muammar Qaddafi, political infighting to fill the power vacuum has plagued Libya.
Mr Dbeibah was appointed under a troubled UN-led peace process last year to lead a transition to elections set for December 2021, but the vote was indefinitely postponed.
In February, Parliament appointed Mr Bashagha, a one-time interior minister, to take over, arguing that Mr Dbeibah's mandate had ended.
But Mr Dbeibah said he will only relinquish power to an elected administration.