TRIPOLI (AFP) - The Islamic State militant group has executed a woman for "witchcraft" and a man accused of spying in its Libyan stronghold, news agencies close to the country's rival authorities said Monday (Dec 14).

IS beheaded the Moroccan woman in a public square and shot dead a Palestinian man for alleged spying in the coastal city of Sirte, said the agency close to the internationally recognised government.

The militants also chopped off a Libyan's hand for stealing, witnesses told it and a rival Tripoli-based news agency.

Libya has had rival administrations since August 2014, when an Islamist-backed militia alliance overran Tripoli, forcing the government to take refuge in the east.

ISIS has exploited chaos and insecurity in Libya since the 2011 fall of Moamer Kadhafi to extend its influence in the North African country.

The group claimed control of Sirte, Kadhafi's hometown some 430 kilometres east of the capital, in June.

The group is trying to spread toward Ajdabiya, a city controlled by loyalist forces and located between Sirte and Benghazi in an area where most of the country's oil and gas terminals are located.

According to a UN report issued in December, ISIS has between 2,000 and 3,000 fighters in Libya, including 1,500 in Sirte.

But the militants face "strong resistance from the population as well as difficulties in building and maintaining local alliances", the report said.