The Islamic State group has no more than 2,000 to 3,000 fighters in Libya and is struggling to expand its foothold in the north African country, a UN report said on Tuesday.

The jihadist group, which controls large swaths of territory in Syria and Iraq, still poses a threat to Libya but the report cited several weaknesses in its operations in what has been widely viewed as an IS rear base.

"ISIL is only one player among multiple warring factions in Libya and faces strong resistance from the population as well as difficulties in building and maintaining local alliances," said the report by a sanctions monitoring team.

Despite several attacks on oil installations in Libya, IS lacks the capacity to seize, hold and manage oil fields or refineries in the country, the report said.

There is no indication that the extremist group is profiting from the refugee smuggling networks in Libya or that it has set up the elaborate extortion rackets that it runs in Syria and Iraq, according to the report.

"ISIL operations in Libya do not appear nearly as lucrative as its operations" in Syria and Iraq, it added.

The Islamic State first appeared in Libya in 2014 when a group of Libyan IS fighters returned from Syria and reorganized in the port city of Derna, declaring eastern Libya to be a province of the caliphate.

A separate group gained control of Sirte in February 2015 but several months later, in June, IS was pushed out of Derna during fighting with other Islamist factions.

There has been growing international alarm about IS’s influence in Libya since a video was released in February showing the horrific beheadings of Egyptian Coptic Christians.

But the report seemed to downplay fears that it was on the verge of a breakthrough in Libya.

"Currently, ISIL seems limited in its ability to expand quickly from its current stronghold," it said.

"While ISIL is able to perpetrate terror attacks in any part of Libya, its limited number of fighters does not allow for rapid territorial expansion."

The report quoted information from several countries stating that IS has no more than 2,000-3,000 fighters in Libya.

At its highest point of influence, the group commanded a force of 1,100 men in Derna but many have since left for Sirte, where IS now has about 1,500 fighters.