Clashes erupted in central Libya on Saturday between Islamic State fighters and a force loyal to a Tripoli-based faction, a military official and residents said.

Islamic State, the militant group which has seized much of Iraq and Syria, has expanded in Libya in recent months, helped by the chaos and lawlessness of a fight for control between two rival governments and their respective allies.

Local supporters of the militants executed a group of Egyptian Christians and have claimed attacks on a luxury hotel, foreign missions and police stations in the capital Tripoli.

On Saturday, Islamic State militants clashed with the al-Shorooq force allied to a Tripoli-based government that was established by the armed faction Libya Dawn.

Libya Dawn seized the capital in August, forcing the internationally recognized government of Prime Minister Abdullah al-Thinni to operate from the east.

"Clashes between Shorooq forces ... and a terrorist group calling itself Islamic State have killed one and wounded two from Shorooq forces," Shorooq spokesman Ismail Shukri said.

"The clashes started when a report arrived that the terrorist group had set up a checkpoint at a coastal road and started inspecting motorists," Shukri said.

"Shorooq forces went to the location to see what was going on but they were attacked by the terrorist fighters," he added.