The unfreezing of £100bn in Libyan assets by the UN this weekend has fired the starting gun for a fierce battle for influence being waged by the country's militias, in which the frontline is set to be Tripoli's international airport.

The glittering prize immediately in prospect is a consignment of several billion dinars, printed in Germany, which is due to be flown into Libya on board five cargo planes. Whoever controls the airport when the cash arrives will be able to levy a hefty security fee for delivering it to the country's central bank. But the fight to control the airport is part of a far wider battle for political and economic dominance in the new Libya; one that pits the various factions who united to overthrow the Gaddafi regime against each other, as well as remnants of the dictator's defeated military.

In theory the decision on Friday by the UN Sanctions Committee and the US to release frozen assets marks, in the words of British foreign secretary William Hague, "another significant moment in Libya's transition". Those sentiments were echoed on Saturday by Leon Panetta, the US defence secretary, on a visit to Tripoli. But the reality is considerably more complicated.

Tripoli airport is currently held by the militia from Zintan, a mountain town 90 miles to the south, who captured it on the way to liberating Tripoli in August. But the Libyan national army, controlled by Gaddafi-era generals, is determined to take control, in what is shaping up to be a defining power struggle. Meanwhile, amid the growing tension the ruling National Transitional Council has become a target for mass protests across the country and the object of deep suspicion outside its Benghazi power base.

Last weekend the army tried to storm the airport and was stopped in a battle at the main airport checkpoint, which left two militiamen wounded and flights suspended as tracer fire arced over the runways. The army tried again midweek, summoning reinforcements from eastern Libya, only for the column to be stopped 200 miles west by units from Misrata, which are allied with Zintan.

More fighting is expected after unidentified gunmen shot and wounded a son of army commander General Khalifa Hifter in a battle outside Tripoli's biggest bank, then kidnapped another on Friday.

Panetta acknowledged that it will "take time" for the NTC to disarm the militias. According to diplomats, the country can move forward only when the national army controls the militias. However, the national army is neither national nor an army.

It was formed in the February revolution in the eastern city of Benghazi by several hundred army officers who defected to the rebels. But most of the army itself remained loyal to Muammar Gaddafi. All of which has left this "national army" with plenty of chiefs but precious few Indians.

The militias, meanwhile, are getting organised. Those of Zintan and Misrata are in effect citizen armies, controlled by their leaders and military councils. Discipline remains a problem, with older members complaining of too many unemployed young men with guns, but order in both cities is more complete than in Tripoli, where gunfire crackles on most nights.

The armies of Misrata and Zintan were the ones that captured Tripoli in August, while the national army was bogged down hundreds of miles away to the east. And the leaderships of these two cities are united in the fear that the NTC, dominated by figures from eastern Libya, will shut them out of power — and deprive them of access to the cash avalanche set to pour into the country.

Last month they forced the government to accept a Zintani as defence minister and a Misratan as interior minister. Following the airport battle, they went a step further, concluding what amounts to a military alliance. As of Friday, three of Tripoli's 11 district militias had signed up to the undeclared pact between the Misratans and Zintanis.

At the airport checkpoint under a flyover, Zintani militiamen, backed by tan jeeps mounting anti-aircraft guns, were busy on Saturday among the concrete road blocks searching vehicles for guns.

"We will hold this position, we have the authorisation," explained Khalid al-Akraj, a young bearded fighter who combines militia duties with running a business back in Zintan. He pointed to a gold and silver star badge worn on his green combat fatigues, a metal army pin dating from the time of Libya's former king, Idris, who was removed by Gaddafi in 1969. "We are not having him (Gaddafi) back, or anyone like him," he said.

Zintan has seven brigades, each with 150 fighters, holding the airport; they are part-timers, rotated between the airport and towns stretching from Zintan along the Jebel Nafusa mountain range to the Tunisian border. Their commander says they can stay at the airport indefinitely.

"The airport is free and it has to stay free," said garrison commander Mustafa al-Araby. "The airport is the only thing that connects Libya to the rest of the world."

Hifter, a former Libyan army general who spent three decades in exile in the US, has other plans. He has perhaps 200 men under his command in Tripoli, but points out that the army is the only military formation authorised by the NTC. His problem is that the NTC is in trouble. Formed, like the army, in Benghazi in the early days of the revolution, the NTC is now the target for mass protests across the country. Demonstrators are united in a single demand — that the NTC come clean about who its members are.

The NTC refuses to say who its members are, or even how many there are. Although it appointed a cabinet last month, policy decisions are taken inside what amounts to a black box. Meetings are held in secret, voting records are not published, and decisions are announced by irregular television broadcasts.

Typical was last week's announcement, which came out of the blue, that the oil and economy ministries would be moved to Benghazi, and the finance ministry to Misrata. Diplomats scoffed at the impracticality of such a scheme, which would leave Libya's administration scattered over hundreds of miles. This opacity reminds some Libyans of how things were run in former times.

This weekend staff at the state broadcaster, LRT, staged a sit-in, claiming that plans to give the station a BBC-style board of governors had been shelved by the NTC, which will instead take direct control of the station.

Officials from the internationally appointed Transitional Finance Mechanism complained last week that Libya has yet to make public accounts from state banks which are to receive the assets windfall.

The man with the power to change things is NTC chairman Mustafa Abdul Jalil, Gaddafi's former justice minister. He is by some distance Libya's most popular politician, but the mantle has started to slip. On Monday he promised to make the NTC's membership public. As of Saturday, it remained secret and the protests are fiercest in Benghazi, supposedly his power base.

Without full disclosure and some sense of transparency, neither the NTC nor its national army are likely to convince the militias to hand over their weapons.

Inside a grimy airport office which sports the green furniture of the former regime, Araby insists his fighters are going nowhere. "We will give up this airport when there is a properly elected government," he said.

Elections for an assembly to draft the constitution are set for next June, but Libya will not have an elected parliament until 2013, leaving Araby and his fighters to contemplate a long wait.

On Saturday, at a news conference with the Libyan prime minister Abd al-Raheem al-Keeb, Leon Panetta said that he was confident that the new government is reaching out to all of the disparate groups and would bring them together so they will be part of "one Libya". As the struggle over Tripoli's airport indicates, there is a still a long way to go to achieve that goal.