* Standoff over oil after navy fires on approaching tanker
* Tripoli struggles to overcome eastern blockade
* Protesters offering to sell crude independently (Adds details from minister, background throughout)
By Ulf Laessing and Ghaith Shennib
TRIPOLI, Jan 8 (Reuters) - Libya may sink tankers trying to load at eastern ports seized by armed protesters in an escalating confrontation over control of oil exports, Prime Minister Ali Zeidan said on Wednesday.
His warning came after Libya's navy fired shots at the weekend to ward off a tanker that the state-run National Oil Corp. (NOC) said tried to load at one port that has been out of government control for six months.
Brent crude rose above $107 a barrel on Wednesday, supported by the new worries over Libyan supplies, which have been slashed since summer by the blockade of three key eastern ports.
Negotiations to end the protests have failed as eastern federalists, whose self-styled Cyrenaica government seeks more autonomy from Tripoli, have threatened to ship oil independently to world markets in defiance of Zeidan.
Protesters on Tuesday said they would guarantee security for vessels docking at the three eastern ports, inviting foreign tankers to load crude and bypass government control.
"Any country, or company, or gang trying to send tankers to take oil from the seized ports without coordinating with the NOC, we will deal with them - even if we are forced to destroy or sink them," Zeidan said. "We warn all countries there will be no leniency."
The confrontation is a major challenge two years after the fall of Muammar Gaddafi in Libya, where former rebels, militias and tribesman have all resorted to force to make demands on a state that is still mapping out the new democracy.
In the east, the Cyrenaica regional authority and its armed protesters have taken over Ras Lanuf, Es Sider and Zueitina ports, which previously accounted for 600,000 barrels per day in crude exports.
On Monday, the Libyan navy said it fired warning shots at a Maltese-flagged tanker trying to reach Libya to load oil at Es-Sider, but the tanker's owners accused Libya forces of firing on them in international waters.
Analysts said they believed it would be difficult for Cyrenaica protesters to find clients to buy oil because of the government view it considers any shipments that bypass its control as illegal.
Stepping up warnings, Oil Minister Abdelbari Arusi told Reuters on Wednesday Libya will sue any foreign firms trying to buy oil from eastern ports and stop doing business with them.
"Any firm... dealing with the armed groups which have closed the oil ports will be sued and banned from any future cooperation," he said. "There won't be any market for them in Libya anymore. We are warning all global and small firms against dealing with the armed groups."
The deepening oil standoff adds to Libya's turmoil as Zeidan struggles to control the armed groups that helped oust Gaddafi in 2011 but which have kept their guns and now demand political power and a bigger share of oil wealth.
The conflict is hurting oil revenues, which fund the OPEC nation's government, which has warned it will be unable to pay public salaries if the standoff continues.
The oil minister said Libya was now producing around 650,000 bpd of oil, of which 510,000 bpd was being exported, after a separate protest in the west ended and unblocked the El-Sharara field there.
Output is still roughly half of the 1.4 million bpd achieved in July before the disruption.
"The Libyan people are dying because of a lack of financing. We need financing to treat sick people, we need it to buy food abroad, overhaul schools, hospitals and to build roads," Arusi said.
"If there is no oil then the Libyan people will die."
Zeidan said he could reshuffle his cabinet this week or next in a bid to counter critics, who are pursuing a parliamentary vote of no-confidence against him.
Two years after the fall of their autocratic leader, Libya's transition to democracy is stranded, its parliament caught in deadlock between Islamist and secular parties, and its new constitution still unwritten.
But the eastern confrontation has heightened worries that Libya might break apart as Cyrenaica and the southern Fezzan region demand political autonomy.
The Cyrenaica oil protesters, led by tribal leader and civil war hero Ibrahim Jathran, have shrugged off Tripoli's warning by inviting foreign companies to buy eastern oil.
"We welcome global oil companies ... The oil security guards will guarantee the safety of tankers," said Abd-Rabbo al-Barassi, prime minister of Jathran's self-declared government in Cyrenaica.
He said a newly founded oil company called Libya Oil and Gas Corp would deal with potential buyers. A new army and coast guard, made up of Jathran's fighters, would secure the ports.
Barassi said his group had nothing to do with the tanker shot at by a Libyan navy on Sunday on its way to Es-Sider.
The group is campaigning for a federal state sharing power and oil revenues between Cyrenaica, Tripolitania in the west, and Fezzan, as was the case in the kingdom that preceded Gaddafi's rule. Oil sales were then shared between the regions.
Tribal leaders have sought to negotiate on behalf of the government with the group holding the ports. These talks have gone nowhere, despite pressure from the tribal leaders, some of who see Jathran as a warlord leading Libya into chaos. (Additional reporting Omar Fahmy; writing by Patrick Markey; Editing by Jane Baird and William Hardy)