(Adds rebel divisions, Benghazi violence, background)
By Ayman al-Warfalli and Feras Bosalum
BENGHAZI/TRIPOLI, Libya, April 3 (Reuters) - Libya has seen evidence of "good intentions" at indirect talks with eastern rebels which could lead to the lifting of their blockage of major oil ports within days, a government minister said on Thursday.
But in an example of the chaos and shifting alliances typical of the OPEC producer, divisions in the rebel camp became apparent on Thursday when a senior member told Reuters he and seven others had quit the rebels' leadership team in a conflict with top leader Ibrahim Jathran.
Hopes have been building in oil markets that an eight-month blockage of major oil exports ports will end ever since rebels and the government said they were close to an agreement.
Any deal will help stabilise the North African country, whose weak government seems unable to control militias who helped oust Muammar Gaddafi in 2011 but kept their guns and made political demands on the state.
"There are good intentions," acting Oil Minister Omar Shakmak told reporters in the eastern city of Benghazi, making clear that the contacts were taking place through tribal leaders who were negotiating with the port rebels.
He did not elaborate, and the government did not provide an update on the status of the talks.
Movement on the issue came after the federalist rebels last month managed to load oil onto a tanker at one port they control and force it out to sea in an attempt to sell the crude.
It was later boarded by U.S. commandos and returned to Libya, killing the rebels' hopes to sell oil independently.
(For a graphic on the blockage, see http://link.reuters.com/fag47v)
The resignations of the eight members of the rebels' so-called politburo on Thursday leaves leader Jathran with a deputy and a self-declared prime minister to finish talks. Other members quit earlier, accusing him of concentrating power.
"Jathran is not consulting his politburo," Essam al-Jahani said, explaining the resignations.
Analysts said a big problem in the talks is how to work around a rebel demand to hold a referendum on whether to introduce a federalist state - devolving some powers and control of oil revenue to regional authorities, as under Gaddafi's predecessor King Idris.
The government fears allowing this might open the door to secession.
Deep divisions exist between the long-neglected east and the capital Tripoli and richer western cities such as Misrata, compounding Libya's rivalries among tribes, competing political factions and brigades of former rebel militias.
Libya's crude output has fallen to around 150,000 bpd from 1.4 million bpd in July when a wave of protests started across the country, whose proximity to Europe just across the Mediterranean makes it a strategic energy supplier.
A deal, if confirmed, would not necessarily end the shutdown of several oilfields in western Libya by a different set of protesters.
Shakmak said the southwestern 340,000 bpd-El Sharara field, the El Feel field and an oil condensates pipeline from the Wafa field to the Mellitah port were all still closed by protesters.
Mellitah is run by Libya's state oil firm and Italy's . In contrast to the east, protesters at western oil facilities, such as El Sharara, are divided into small groups lacking joint leadership with whom Tripoli can bargain.
Some pipelines have been damaged, officials told reporters.
In another sign of growing turmoil, a hospital in Benghazi on Thursday called on Ansar Shariya, an Islamist militia labelled a terrorist organisation by Washington, to protect its premises while health workers went on strike to protest against a series of shootings inside clinics, staff said.
The Jala State Hospital asked for protection after repeated shootings and a car explosion outside its building, a hospital spokesman said.
The United States has blamed members of Ansar Shariya for an Islamist assault on its consulate in September 2012, during which its ambassador to Libya and three Americans were killed.
Across the city, staff at the three main hospitals went on strike after gunmen started a shooting in the emergency ward of the Benghazi Medical Center (BMC), the biggest hospital. (Reporting by Ayman al-Warfalli, Ulf Laessing, Ahmed Elumami and Feras Bosalum; Editing by David Evans and Sonya Hepinstall)