* Tensions high after navy fires at oil tanker
* Eastern federalists want more autonomy, oil share
* Oil port protests have drained public finances
By Ghaith Shennib
TRIPOLI, Jan 14 (Reuters) - Libya's Prime Minister Ali Zeidan said the government would give mediators a chance to end a standoff with protesters blockading eastern oil ports, seeking a peaceful solution even after an escalation of the dispute over crude exports.
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 regional autonomy and a greater share of oil.
Two years after the fall of Muammar Gaddafi, the port dispute is the most serious challenge to the fragile central government as it struggles to control former militias and rebels, who refuse to bow to Tripoli's authority.
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 Libya's General National Congress parliament and from tribal leaders have reached out to protesters but with little success.
"We are now in touch with mediators who intend to dialogue with 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, which is putting a strain on public finances that depend almost completely on oil revenue.
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, to demand more political autonomy for the region and a share of Libya's crude sales.
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 its production to rise again to around 328,00 bpd, according to the state-run National Oil Corp.
Political solutions are complicated in Libya, where the General National Congress and its members have yet to complete vital parts of the transition to democracy since Gaddafi's fall, including the writing a new constitution.
The parliament is deadlocked between secular and Islamist parties, while militias that once helped fight Gaddafi have refused to disarm, claiming that Tripoli is too weak to guarantee stability. (Writing by Patrick Markey; editing by Jane Baird)