TRIPOLI, Aug 28 (AFP) - Libya's internationally recognised prime minister has sacked his top diplomat after she met her Israeli counterpart, with news of the encounter triggering protests in a country that does not recognise Israel.

Oil-rich Libya, which plunged into chaos after dictator Muammar Gaddafi was toppled and killed in a 2011 NATO-backed uprising, has been divided since 2014 between the UN-supported government of Prime Minister Abdelhamid Dbeibah in Tripoli and a rival administration based in the country's east.

Analysts who spoke to AFP appeared to agree that Najla al-Mangoush was the "fall person" for decisions made by Libya's rival leaders, and linked the meeting with United States efforts to pressure more Arab countries to normalise ties with Israel.

Al-Ahrar private news channel, citing a government source, said Mangoush had been fired following a meeting last week in Rome with Israeli Foreign Minister Eli Cohen.

The Palestinian embassy in Tripoli also reported her dismissal, saying it had been announced by Dbeibah during a visit Monday to the mission. Dbeibah also declared "his rejection of normalisation with Israel" and Libya's total support for the Palestinian people, the embassy said.

In the east, Libyan lawmakers demanded an investigation into the meeting at a special session during which they wore the chequered black-and-white Palestinian scarf.

The Mangoush-Cohen meeting sparked protests Sunday night in Tripoli and other cities, when demonstrators blocked roads with burning tyres and waved Palestinian flags.

Before visiting the Palestinian embassy, Dbeibah's government said Mangoush had been "provisionally suspended and subject to an 'administrative investigation'", while in Israel Cohen confirmed the meeting took place.

Mangoush's whereabouts were uncertain on Monday, following social media reports she had flown to Turkey as protests flared.

Libya's Internal Security Agency (ISA) said she had not been authorised to leave the country and was on a "travel ban list" awaiting investigation.

Turkey's Anadolu news agency, citing security sources, said Mangoush had already left for Istanbul following the diplomatic furore.

The Libyan foreign ministry, in a statement, defended the meeting with Cohen as a "chance and unofficial encounter".

Mangoush had reiterated "in a clear and unambiguous manner Libya's position regarding the Palestinian cause", it said, accusing Israel of trying to "present this incident" as a "meeting or talks".