Tripoli city leaders on Sunday called for street protests and strikes at shops, schools and universities to press Libya's government to drive out militiamen blamed for clashes that killed at least 45 people.

Libyan Prime Minister Ali Zeidan's armed forces are struggling to control militias, Islamist militants and other former fighters who refuse to disarm after helping to oust Muammar Gaddafi in a Nato-backed uprising two years ago.

Violence broke out on Friday when militiamen from the coastal city of Misrata opened fire on protesters marching on their brigade quarters in Tripoli to demand they leave the capital.

Dozens of people were killed in the clashes that followed - the deadliest street fighting in Tripoli since Gaddafi's fall. Misrata gunmen and rival militias clashed again on Saturday to the east of the capital, killing one more.

Saadat Al-Badry, the head of Tripoli's local council, told Reuters, that city leaders wanted all armed groups from outside Tripoli to leave the capital and demanded an investigation into Friday's violence.

"We have declared a strike for three days from today, but if our demands are not met we will continue," he said. "We will not negotiate with them. Things are as clear as the sun, we want a decision."

Backing up those demands against powerful and well-armed militias will be difficult for Zeidan's government, whose nascent armed forces are still training with help from the United States and its Nato partners.

Zeidan himself was abducted by a government-payrolled militia group last month but freed unharmed after a few hours.

Many stores, schools and universities were closed in the capital on Sunday - normally a working day in Libya - and some in neighbourhoods. Residents set up barricades of metal, wood and tyres to protect their streets and join the protest.

Militiamen and former fighters are often employed by the government to protect ministries and government offices. But gunmen remain loyal to their commanders or tribes and often clash in rivalries over control of territories.

Militias tied to an autonomy movement for eastern Libya have taken over oil ports for months, cutting off about half of the crude shipments from the Opec oil producer.

Fighters from Misrata are part of the Libya Shield Force militia and Islamist fighters from the fertile coastal area to the east of the capital around Misrata city.

But they have recently been more isolated in Tripoli after some of their fighters were involved in personal disputes with former allies in the Supreme Security Committee, an Islamist militia based in Mittiga airbase in the east of the capital.

Other militias are also rivals of the Misrata group, including the powerful Zintans, a loose alliance of more secular Bedouin tribes from the desert interior, who control an area around Tripoli's international airport. - Reuters