The United States is increasingly concerned about the growing presence and influence of the Syria-based Islamic State movement in Libya, according to  officials and a State Department report.

The officials said what they called "senior" Islamic State leaders had traveled to the country, which is wracked by civil war, to help recruit and organise militants, particularly in the cities of Derna and Sirte.

Since late January, Islamic State militants have carried out attacks, including a car bombing and siege at the Corinthia, a luxury hotel in Tripoli, and an attack on the Mabruk oilfield south of Sirte, according to a report circulated this week by the State Department's Diplomatic Security Bureau.

The militants also posted on the web images of the beheading of 21 abducted Egyptian Coptic Christians on a Libyan beach.

The State Department document said estimates of the number of Islamic State fighters operating in Libya ranged from 1,000 to 3,000.

Around 800 fighters were based in the Derna area alone, the report said, including up to 300 who previously fought in Syria or Iraq.

US officials said that because of its strategic position, Libya had become a springboard for would-be fighters from across North Africa wanting to link up with the Islamic State. They could travel from there to Syria for frontline experience.

The State Department assessment, whose existence was first reported by the Washington Free Beacon website, said that the disintegration of central authority in Libya "has given ISIL an opening to establish a legitimate foothold".

The report said Islamic State had only had limited success in capturing and holding territory in Libya.

US officials said Libya Dawn, an Islamist, but non-Jihadist, movement based in the city of Misurata, was mounting a counter-attack against Islamic State forces, a development which the United States considered encouraging.

Islamic State has also endorsed, or received expressions of loyalty, from other militants around the region, including factions based in Nigeria, Yemen, Afghanistan, Pakistan and Egypt's Sinai Peninsula.

US agencies are evaluating evidence that appears to tie Islamic State to the militants who killed 20 foreign tourists on Wednesday at a museum in Tunis, the capital of Libya's western neighbour Tunisia.