* Son says Gaddafi would quit if he loses vote
* Libyan PM says Gaddafi would have no reason to step down
* NATO resumes bombing in Tripoli
By Nick Carey
TRIPOLI, June 17 (Reuters) - NATO planes resumed bombardments of Tripoli after Muammar Gaddafi's son said the Libyan leader was willing to hold elections and step aside if he lost, an offer rejected by rebels and the United States.
Gaddafi's son Saif al-Islam told an Italian newspaper that the elections could be held within three months and transparency could be guaranteed through international observers.
He said his father would be ready to cede power if he lost the election, though he would not go into exile.
But Prime Minister Al-Baghdadi Ali Al-Mahmoudi appeared to throw the potential concession into question, saying on Thursday that the leader of the revolution was not concerned by "any referendum".
A visiting Russian envoy said the Libyan leadership had reiterated that Gaddafi's departure was a "red line".
The rebel leadership in the eastern stronghold of Benghazi rejected Gaddafi's son's election offer.
"We tell him (Saif al-Islam) that the time has passed because our rebels are at the outskirts of Tripoli, and they will join our people and rebels there to uproot the symbol of corruption and tyranny in Libya," rebel spokesman Abdel Hafiz Ghoga told Al Jazeera television.
A U.S. State Department official also dismissed the election idea, saying it was "a little late for that".
The proposal -- which follows a series of moves the Libyan leader's officials portray as concessions but Western powers dismiss as ploys -- comes at a time when frustration is mounting in some NATO states at slow military progress.
Rebel advances towards Tripoli have been slow, while weeks of NATO strikes pounding Gaddafi's compound and other targets have failed to end his 41-year-old rule.
In the latest raids, eight loud explosions were heard in southeast and southwest Tripoli late on Thursday and planes could be heard overhead. Libyan state television said NATO had hit targets in the Al-Ferjan district of the city.
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The NATO intervention in Libya has been going on for nearly 13 weeks -- longer than many of its backers anticipated -- and the strains are beginning to show within the alliance.
NATO officials have said they may not have the resources for a sustained campaign, and Republicans in the U.S. Congress have questioned the legal grounds for continued U.S. involvement.
House of Representatives Speaker John Boehner said lawmakers had options for dealing with the conflict, including "the power of the purse" -- an implicit threat to cut off funding.
Libya-watchers say Gaddafi is using his political skills, honed during decades when he was able to survive despite being an international pariah, to try to exploit divisions.
Adding to the pressure on NATO, Russia and China issued a declaration underlining their concerns about the air strikes.
Russia and China decided in March not to use their veto power at the United Nations to block intervention on Libya, but have said NATO risks going beyond the U.N.-authorised mandate to protect civilians.
Rebel forces are now fighting Gaddafi's troops on three fronts: in the east of the country around the oil town of Brega, on the road to Tripoli from the rebel-held port of Misrata, and in the Western Mountains southwest of Tripoli.
They have made slow but important gains in the past few weeks in the mountains and near Misrata, bringing the front closer to Tripoli from the east and southwest.
Gaddafi has called the rebels "rats" and says NATO's campaign is colonial aggression to steal Libya's oil.
In Misrata, the rebels say they are recruiting fighters from the government-held neighbouring town of Zlitan before advancing.
Zlitan, just 160 km (100 miles) from Tripoli, is the next major town on the Mediterranean coast road to the capital. Capturing it would be a major victory.
Kalefa Ali, a rebel spokesman in the Western Mountains town of Nalut, told Reuters that despite shelling by Gaddafi forces in Nalut and the Wazin border crossing with Tunisia on Thursday, the rebels would push forward.
"We think we will be able to drive Gaddafi's forces out of the Western Mountains altogether within days," he said.