AL-QAWALISH, Libya (Reuters) - Rebel fighters seized a village south of the Libyan capital and another group advanced toward Tripoli from the east on Wednesday in the biggest push in weeks toward Muammar Gaddafi's main stronghold.
Rebels firing their rifles into the air in celebration poured into the village of Al-Qawalish, 100 km (60 miles) southwest of Tripoli, after a six-hour battle with pro-Gaddafi forces who had been holding the town.
Rushing through an abandoned checkpoint where government troops had left tents and half-eaten bread in their rush to get away, the rebels ripped down pro-Gaddafi flags.
Farther north, rebels pushed westward from the city of Misrata to within 13 km of the center of the town of Zlitan, where large numbers of pro-Gaddafi forces are based.
But they came under artillery fire. Doctors at the al-Hekma hospital in Misrata said 14 fighters had been killed on Wednesday and about 50 were injured.
The advances came amid reports that Gaddafi -- under pressure from a five-month uprising against his rule, sanctions and a NATO bombing campaign -- was seeking a deal under which he would step down.
His government has denied any such negotiations are underway, and NATO's chief said he had no confirmation that Gaddafi was looking for a deal to relinquish power.
A Libyan official told Reuters on Wednesday there were signs a solution to the conflict could be found by the start of August, though he did not say what that solution might involve.
In the rebel-held cities of Benghazi and Misrata, thousands demonstrated against Gadaffi, waving European and rebel flags and calling for the end of his four-decade rule.
The rebel advances followed weeks of largely static fighting. Heavily armed Gaddafi forces still lie between the rebels and Tripoli, and previous rebel advances have either bogged down or quickly turned into retreats.
But with Al-Qawalish now in rebel hands, they can advance northeast to the larger town of Garyan, which controls the main highway leading into Tripoli. Libyan state television reported on Wednesday that NATO hit targets in Garyan as well fuel tanks in the town of Brega, 200 km (130 miles) west of Benghazi.
The previous big advance in the region was last month, when rebels pushed 20 km (12 miles) north from their base in the Western Mountains to the town of Bir al-Ghanam.
At the frontline on the outskirts of Zlitan, a unit of fighters had built a sand-bank behind which they could shelter while firing at government troops. There were still sounds of intermittent shelling as night fell.
Unit commander Tarek Mardi, a 36-year-old former banker, said pro-Gaddafi forces had tried to push his fighters back but they had held their ground.
"Why isn't NATO doing its job, where are the Apaches?" he asked, referring to the attack helicopters the alliance had deployed to Libya. "We are protecting our people, our country. We want to save our land from Gaddafi. He is a criminal."
More than 100,000 rebel supporters spilled into the streets of Benghazi waving European and rebel flags and chanting slogans against the Libyan leader.
Gaddafi, who has ruled oil producer Libya for 41 years, says the rebels are armed criminals and al Qaeda militants. He has described the NATO campaign as an act of colonial aggression aimed at stealing Libya's oil.
A Russian newspaper this week quoted what it described as a high-level source as saying Gaddafi is sounding out the possibility of stepping down on condition there was a political role for one of his sons.
A Libyan government spokesman denied that report, saying Gaddafi's future was not up for negotiation.
Deputy Foreign Minister Khaled Kaim told Reuters in Tripoli that a solution to the conflict could be found before the Muslim holy month of Ramadan begins early in August.
"There are signals that the crisis will find a solution in the coming weeks. We will do whatever possible so that our people will spend Ramadan in peace," he said.
"Currently the key hurdle to a solution is the NATO military campaign, and we hope that our friends in the African Union organization will do whatever possible to convince it to stop its aggression against our people."
NATO Secretary General Anders Fogh Rasmussen said he had no confirmed information that Gaddafi had sounded out the possibility of stepping down.
"But it is quite clear that the end state must be that he leaves power," Rasmussen told a news conference in Brussels.
Additional reporting by Nick Carey in Misrata, Hamid Ould Ahmed in Algiers, Lamine Chikhi in Tripoli, David Brunnstrom in Brussels, Maria Golovnina in Benghazi, Joseph Nasr in Berlin and Moscow bureau; Writing by Christian Lowe and David Dolan; Editing by Diana Abdallah