* Militias demand Zeidan step down, want vote
* Eastern federalists want more autonomy, oil share
* Oil port protests have drained public finances
By Ghaith Shennib
TRIPOLI, Jan 14 (Reuters) - Former Libyan militia fighters stormed parliament on Tuesday and fired in the air to try to force assembly members to take a no-confidence vote against Prime Minister Ali Zeidan.
The brief incident highlighted Libya's struggle to contain former rebels and militias who often turn to force to make demands on the weak central government two years after they helped oust Muammar Gaddafi in a civil war.
About 30 militiamen, most armed with rifles, forced their way into the General National Congress (GNC) parliament compound in Tripoli, opening fire and briefly blocking one entrance before assembly members escaped via another route, witnesses and security sources said.
"We were in the middle of discussions, when armed protesters stormed into the GNC demanding that we hold a vote of no confidence," Saad Bin Sharada, a GNC member, told Reuters.
Political transition is messy in Libya, where parliament has yet to complete key steps to democracy since Gaddafi's fall in 2011, including the drafting and approval of a new constitution.
Parliament is deadlocked between secular and Islamist parties over a roadmap to democracy, while militias that once helped fight Gaddafi have refused to disarm, claiming Tripoli is too weak to guarantee stability.
Opponents of Zeidan, who was himself briefly abducted last year by former rebels now on the government payroll, are trying to muster support for a vote of no confidence against him. But even critics say there is no clear candidate to replace him.
Two years after the NATO-backed war, the most serious challenge comes from the east, where a former rebel commander and hero of the uprising against Gaddafi has taken over three key oil ports to demand more regional autonomy.
Zeidan said on Tuesday the government would give mediators a chance to end a standoff with protesters blockading eastern ports, seeking a peaceful solution even after an escalation of the dispute last week.
MEDIATION VERSUS FORCE
Libya's navy last week fired warning shots at an oil tanker the government said tried to load crude at one of the terminals seized by protesters who are demanding more political independence from Tripoli and a greater share of oil revenues.
With Libya's leadership hamstrung by infighting and a nascent army still in training, Zeidan's government may have little option but to seek help from mediators in trying to negotiate an end to the crisis.
For several months, delegations from the GNC and tribal leaders have reached out to protesters, but with little success.
"We are now in touch with mediators who intend to (talk to)those occupying the ports," Zeidan said at a press conference.
"We have two solutions: Through force or peaceful means. We preferred the peaceful way. We have found some people who say they can do this, and we will give them the chance."
Libya's crude production last week was at around 600,000 barrels per day, down from 1.4 million bpd, putting a strain on public finances that depend almost completely on oil earnings.
Eastern oil protesters in August took over the ports of Ras Lanuf, Es-Sider and Zueitina, which previously accounted for 600,000 bpd in exports.
Eastern federalists from the self-declared Cyrenaica government promise that ships can safely dock at the ports they control, dismissing Zeidan's warnings that tankers may be destroyed if they try.
But even with the government's limited military resources, experts say, protesters may struggle to find tanker operators willing to risk entering ports to load cargoes of discounted crude, which the government would see as an act of piracy.
Negotiations have had more success in the west and the south, where protests ended at the major El Sharara field, allowing production to rise again to around 328,000 bpd, according to the state-run National Oil Corp.