By Ghaith Shennib

TRIPOLI (Reuters) - Libya's deputy intelligence chief was kidnapped outside Tripoli's international airport on Sunday, a month after the prime minister was snatched by militiamen.

The kidnapping, and clashes in the capital that have killed dozens of people, highlight Libya's struggle to curb rival militias and hardline Islamists who refuse to disarm two years after they helped oust Muammar Gaddafi in a NATO-backed uprising.

Mustafa Noah, the head of agency's espionage unit, was bundled into a vehicle in the car park, and had no bodyguards with him at the time, two security sources said, without giving further details on the attackers or their motives.

The kidnapping, and clashes in the capital that have killed dozens of people, highlight Libya's struggle to curb rival militias and hardline Islamists who refuse to disarm two years after they helped oust Muammar Gaddafi in a NATO-backed uprising.

No group claimed responsibility for the abduction, but militias have snatched officials in the past to get political leverage. Prime Minister Ali Zeidan was briefly abducted by a militia group on the government payroll last month.

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 the clashes on Friday and Saturday that killed 46 people.

Violence broke out 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 - the deadliest street violence in Tripoli since Gaddafi's fall.

Misrata gunmen and rival militias clashed again on Saturday to the east of the capital, killing one more.

Tripoli was calmer on Sunday. Misrata militia fighters of the Gharghour brigade had withdrawn from their base in the city, at least temporarily and the military had taken over the area, witnesses and the government said.

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

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

But in a sign of rising tensions, Misrata City leaders threatened to withdraw their members from the country's cabinet, national congress and pull back their former fighters who had been helping provide security in the capital.

"They forgot about the rebels,and so we will give the opportunity for the government to show us what will they do with the army and police," said Attia Al-Drayni, deputy head of Misrata's local council.

RIVAL MILITIAMEN

Many stores, schools and universities were closed in the capital on Sunday - normally a working day in Libya. Residents set up barricades of metal, wood and tires 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 over the control of territory.

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, a group of more Islamist-leaning fighters from the fertile coastal area around Misrata city

But they have recently become more isolated in Tripoli after some of their fighters were involved in 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 airport.

(Writing by Patrick Markey; Editing by Alison Williams and Jackie Frank)