(Adds detail on protests)
TRIPOLI, Jan 3 (Reuters) - Flights were suspended at the only functioning airport in Libya's capital Tripoli on Friday due to rocket fire and shelling, as protesters in the east of the country demonstrated against Turkish military support for their rivals.
Turkey's parliament voted on Thursday to allow troops to be sent to support the internationally-recognised Government of National Accord (GNA) in Tripoli, deepening fears of an escalation of fighting in the North African country.
The GNA has sought Turkish support as it fends off an offensive by General Khalifa Haftar's forces, which control the east and swept through southern Libya in early 2019.
Haftar's forces said on Friday they had carried out air strikes in several locations, including south of the city of Sirte and in Tripoli.
Sirte lies in the centre of Libya's coastline, on the dividing line between the warring factions.
Haftar's Tripoli offensive quickly stalled in the outskirts of the capital, but led to increased international involvement in the conflict. Turkey has backed the GNA while Haftar has received support from the United Arab Emirates, Egypt and Jordan.
Russian military contractors have also been deployed with Haftar's Libyan National Army for several months, diplomats and analysts say.
There were protests in several cities and towns in eastern Libya against the Turkish parliament's decision.
In Benghazi, where about 3,000 people took to the streets, protesters said they had turned out to oppose a Turkish "invasion" of Libya, which was part of the Ottoman Empire before coming under Italian occupation.
"We deplore and denounce (the Turkish decision) and affirm that Libya will remain an independent state and won't agree to return to the Ottoman Empire once again," said protester Mahmoud al-Barasy.
Three subsidiaries of Libya's National Oil Corporation (NOC) which operate in areas under Haftar's control -- Ras Lanuf Oil and Gas Company, Sirte Oil Co and Arabian Gulf Oil Company (AGOCO) -- issued statements saying they would boycott Turkish companies.
An engineer from Ras Lanuf said one Turkish company had been carrying out contracting work at Ras Lanuf port since 2017, but it was unclear what immediate impact the statements would have.
Mitiga Airport has been repeatedly closed and reopened in recent years because of risks from shelling and air strikes, reopening most recently on Dec. 12 after a closure of nearly 3-1/2 months.
It closed early on Friday because of rocket fire nearby, before reopening briefly and then shutting again due to shelling, airport and airline officials said.
Tripoli's main international airport was closed and partially destroyed in an earlier round of fighting in 2014, when Libya split into rival political and military alliances based in the capital and the east. (Reporting by Hani Amara, Ahmed Elumami and Ayman al-Warfalli; Writing by Aidan Lewis; Editing by Edmund Blair and Louise Heavens)