* Depot with millions of litres of fuel blazing near airport
* Benghazi calmer after Islamist militants seize army base
* British diplomats prepare to close embassy in Tripoli (Adds British navy evacuation)
By Patrick Markey
TRIPOLI, Aug 3 (Reuters) - Libya's government said more than 20 people had been killed in the latest battles between factions seeking to control Tripoli airport on Sunday, while fighting led to a huge fire raging nearby at the city's fuel depot.
Rival factions allied to brigades from the towns of Misrata and Zintan have been fighting for nearly three weeks over control of the capital's airport in the worst violence since the 2011 NATO-backed civil war that ousted Muammar Gaddafi.
A steady stream of foreigners have been evacuated from the North African state since the fighting began last month, and on Sunday a Royal Navy ship took away around 100 British citizens, families and others from Tripoli.
The city was quieter on Sunday morning except for sporadic blasts. But eight gas tanks hit by a rocket on Saturday at a fuel depot near the airport were still burning, sending a huge pall of smoke up over the capital.
"Tripoli's hospitals received 22 bodies (on Saturday) and 72 people were wounded," Libya's government said in a statement on Sunday.
"Mediating committees are still trying to stop the violence and return Tripoli to normal. They have faced difficulties because of the stubbornness of the militias attacking the city."
The Oil Ministry issued a warning that the burning fuel tanks could explode and called on the Health Ministry to be prepared in case of casualties.
Most Western governments have evacuated their embassies after clashes erupted in Tripoli and the eastern city of Benghazi more than two weeks ago, fearing that Libya is sliding back into civil war.
Britain, one of the last Western countries to keep its embassy open, said late on Friday that it would evacuate its diplomatic staff to Tunisia and close the embassy on Monday.
Britain's ministry of defence said in a statement the Royal Navy's HMS Enterprise arrived in Tripoli on Sunday to evacuate British nationals and families. An embassy official said around 110 people were transferred to the ship.
Islamist-leaning brigades allied to the western port town of Misrata have been attacking Tripoli airport with rockets and artillery to oust rivals from the mountain town of Zintan who have controlled it since the city fell in 2011.
Misrata and Zintan rebel fighters once battled side by side to topple Gaddafi. But three years on they have refused to disarm and their rivalry has exploded in a violent struggle over who dominates Libya after the dictator's demise.
Libya's government and weak military have been unable to control the armed factions, who often claim semi-official status approved and paid for by ministries, and control huge stockpiles of Gaddafi-era weapons, tanks and missiles.
Firefighters have been battling to extinguish the massive blaze at the fuel depot that supplies Tripoli and that has been hit twice in a week by rockets and shell fire.
Most of Tripoli has been calm, with fighting mainly restricted to the de facto frontlines in the south and parts of the west of the city. Fuel prices, though, have soared on the black market as fighting has caused fuel shortages.
Fighting with Grad rockets and artillery over Tripoli has closed the airport and prompted the United States, the United Nations and most European governments to pull their diplomats out of the North African state.
Western governments hope Libya's newly elected parliament, which is meeting in the eastern city of Tobruk, will create some space for the warring factions to reach a political settlement and a ceasefire.
But the sides are bitterly polarised around two loose confederations of militias and their political allies, with rival visions for a post-Gaddafi Libya.
The last parliament, known as the General National Congress, was stormed numerous times by different militia brigades trying to pressure lawmakers on political decisions.
Fighters from the mountain town of Zintan, including ex-Gaddafi forces in the Qaaqaa and Al-Sawaiq brigades, are allied with the National Forces Alliance movement led by a former Gaddafi official.
Leaders of the fighters from Zintan say their brigades are a bulwark against rivals they brand Islamist extremists trying to control Libya.
The Misrata brigades are aligned with the Justice and Construction party and the Muslim Brotherhood. They say they are fighting to clean out remnants of Gaddafi's army.
Complicating matters even more, in Benghazi in the east an alliance of Islamist fighters and ex-rebels banded together to battle Libyan armed forces, seizing a special forces military base last week and pushing the army outside of the city.
They joined forces when a renegade ex-army officer and former Gaddafi ally, Khalifa Haftar, allied himself with regular special forces in the city to launch a campaign to oust Islamist militants from Benghazi.
Those Islamists, Ansar al-Sharia, are branded a terrorist organisation by Washington and blamed for the attack on the U.S. mission in Benghazi in 2012, in which the U.S. ambassador and three other Americans died. (Additional reporting by Aziz El Yaakoubi; Editing by Susan Fenton and Hugh Lawson)