* At least four fighters killed, rebels say
* Rebels say were outnumbered
* Contested town near Tripoli eerily quiet
BENGHAZI/ZAWIYAH, Libya, June 13 (Reuters) - Rebels fighting against Libyan leader Muammar Gaddafi say they were repulsed by his forces in a battle to retake the eastern oil town of Brega, suffering at least four dead.
In the west, rebels said they were fighting Gaddafi's forces for a second day in the town of Zawiyah on Sunday, bringing the revolt against his rule closer to the capital.
The rebels said they had lost at least four killed in fighting between Brega and Ajdabiyah. At least 65 fighters were wounded, doctors at the hospital in the rebel stronghold city of Benghazi said.
"We attacked them first but they attacked us back. We tried to get to Brega but that was difficult," Haithan Elgwei, a rebel fighter, said after returning from the front with the wounded.
"NATO (aircraft) were covering us from above but Gaddafi troops fired rockets and mortars outside Brega," Akram, 24, a wounded fighter, said.
"We will not retreat. We look forward to taking Tripoli," he added.
The fresh outbreak of fighting in Zawiyah, west of Tripoli and home to a big oil refinery, marks the closest the armed rebellion has come to Gaddafi's stronghold in the capital for months.
Reporters taken by the government to see Zawiyah, which saw intense fighting at the start of the anti-Gaddafi uprising in February and has changed hands several times, found it eerily quiet on Sunday, with almost no one in sight.
On Saturday, Libyan government spokesman Moussa Ibrahim said there was "no serious fighting" there.
On Sunday, he told reporters that no more than 100 rebel fighters who had attacked to the west of the city were holed up after suffering losses and the government was trying to negotiate their surrender.
"They were defeated after a few hours of scattered skirmishes with the army," he added.
Not long after the reporters left Zawiyah, rebel spokesman M'hamed Ezzawi said by phone there was heavy fighting 400 m (yards) from the main square.
"The brigades are using heavy weapons. They are better equipped than the revolutionaries," he said. "We have no statistics so far as to the number of martyrs but there are at least seven wounded among the revolutionaries."
"DAYS ARE NUMBERED"
After the nationwide rebellion against Gaddafi's 41-year rule erupted in February, his security forces snuffed out the rebels in Zawiyah, a prelude to the revolt elsewhere in Libya losing its initial momentum.
Three months later, the war has shifted again, with Gaddafi's grip on power weakened by defections, the impact of sanctions on supplies and NATO air strikes that have struck his compound in Tripoli.
Australian Foreign Minister Kevin Rudd, in an interview with Reuters, said there was a growing confidence that Gaddafi's "days are numbered".
Libyan state television broadcast images of Gaddafi -- who has been keeping a low profile since NATO began its air strikes -- meeting Kirsan Ilyumzhinov, president of the international chess federation.
Ilyumzhinov, quoted by Russian news agencies, said he played a game of chess in Tripoli with the Libyan leader, who told him he had no intention of leaving his country.
The United Arab Emirates said it had recognised the rebel Transitional National Council, based in Benghazi, joining a small but growing list of states which view the council as Libya's legitimate representatives.
Gaddafi has called the NATO intervention with warplanes and attack helicopters an act of colonial aggression aimed at grabbing Libya's plentiful oil.
In Tripoli residents have told Reuters of anti-Gaddafi protests, though these have been quickly dispersed by his security forces.
"The districts of Tripoli are waiting for a signal so they can all rise up together," said a resident of the city who did not want to be named for fear of reprisals.
NATO member states are keen for a quick resolution in Libya because their voters do not want another long, costly conflict along the lines of those in Iraq and Afghanistan.
(Additional reporting by Hamid Ould Ahmed in Algiers, Mussab Al-Khairall in Tripoli, Matt Robinson in Misrata, Kate Kelland in London, Andrew Hammond in Dubai and Jan Strupczewski in Brussels; Writing by Michael Roddy; Editing by Sanjeev Miglani)