Oil-rich Libya, which does not recognise Israel, plunged into years of chaos after a NATO-backed uprising toppled and killed dictator Moamer Kadhafi in 2011.

It 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.

Angry protesters took to the streets of Tripoli and other western cities of Libya on Sunday night, blocking roads with burning tyres and waving Palestinian flags, after it emerged that Najla al-Mangoush had met with her Israeli counterpart in Rome last week.

Hours after Israeli Foreign Minister Eli Cohen said the "unprecedented" meeting had taken place, Mangoush was "provisionally suspended and subject to an 'administrative investigation'", Dbeibah's government said.

On Monday, the Internal Security Agency (ISA) said Mangoush had not been authorised to leave Libyan territory after reports on social media that she had flown to Turkey overnight.

Internet users had posted the tracking details from the FlightRadar website of a flight said to be carrying Mangoush from Mitiga airport in Tripoli to Istanbul.

"Surveillance cameras will prove this" is false, the ISA said in a statement.

Mangoush "is on the travel ban list until she submits to the investigation", said the security agency.

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

It said the minister had reiterated "in a clear and unambiguous manner Libya's position regarding the Palestinian cause".

It accused Israel of trying to "present this incident" as a "meeting or talks".

The Israel foreign ministry statement had quoted Cohen as saying that the two discussed "the importance of preserving the heritage of Libyan Jews, which includes renovating synagogues and Jewish cemeteries in the country".

"Libya's size and strategic location offer a huge opportunity for the State of Israel," he added.

The statement said the meeting in Rome had been hosted by Italian Foreign Minister Antonio Tajani.

Tajani's office on Monday referred all questions to the Libyan and Israeli authorities. However, an Italian diplomatic source said the Italian minister had not himself been present at the meeting.

Israel has normalised relations with some Arab countries in recent years as part of US-backed deals known as the Abraham Accords.