The statement late Saturday came after the IS affiliate seized control of a new neighbourhood in Sirte. The militants shelled the area, killed a senior cleric and hung the bodies of prisoners over bridges.
"The Libyan government, unable to ward off these terrorist groups because of the arms embargo, and out of its historic responsibility toward its people, calls on brotherly Arab countries ... to launch airstrikes against specific targets of (IS) locations in Sirte in coordination with our concerned bodies," the statement said.
The government also condemned the failure of the international community to take action against the group's rise in Libya.
The Arab League said it will hold an emergency meeting on Libya on Tuesday.
Egypt has joined Libya's government in calls for international intervention there against IS. Egypt has carried out airstrikes inside Libya, including in February after Islamic State militants killed 21 Egyptian hostages there.
The IS affiliate posted pictures on social media showing booty it seized from the neighborhood in Sirte, including vehicles and ammunition.
Fighting began earlier this week after a rival Islamist group, backed by a local tribe, refused to pledge allegiance to IS and called for a revolt.
Residents fled as IS militants took over the area. Awad Salem, whose family remains in the city, said IS fighters seized homes, refusing to allow residents to return until they search them for weapons.
Libya has slid into chaos since the 2011 overthrow and killing of longtime dictator Moammar Gadhafi. It is now divided between an elected parliament and government in the east, and an Islamist militia-backed government based in Tripoli.