Bombings in the town of Quba, which is controlled by the paramilitary force of former General Khalifa Haftar, added to concerns that ISIL has spread beyond the battlefields of Iraq and Syria and established a foothold in North Africa.
ISIL claimed responsibility for the suicide bombings in Quba, about 250km east of Benghazi, but said there were only two attacks, while the government said there were three.
ISIL released a video on Sunday that showed the beheading of 21 Egyptian Christians who were abducted in Sirte, and Egypt responded on Monday with air strikes on Derna, a city about 30km from Quba.
The coastal Mediterranean cities of Sirte and Derna are under ISIL's control at present.
Mohammed Hegazi, an army spokesperson, said one attacker drove an explosives-packed ambulance into a petrol station where motorists were lined up, Al Jazeera reported.
"Imagine a car packed with a large amount of explosives striking a petrol station; the explosion was huge and many of the injured are in very bad shape while the victims' bodies were torn into pieces," Hegazi said.
Two other bombers detonated vehicles next to the house of the parliament speaker and the nearby security headquarters, Hegazi said.
Libya is split between two rival parliaments and governments.
The elected and internationally recognised parliament has been forced to relocate to the eastern city of Tobruk near the Egyptian border because Tripoli has been overrun by the Islamist and tribal groups.