* French minister: rebels must negotiate peace deal now

* Gadhafi's govt in talks with France - Saif al-Islam

* Washington says firm in belief Gadhafi must go

* Differences widening inside Western alliance

TRIPOLI - France's defence minister said it was time for Libya's rebels to negotiate with Muammar Gadhafi's government, signalling growing impatience with progress in the conflict.

Gadhafi's son, in an interview with an Algerian newspaper on Monday, said his father's government was in talks with the French government. There was no immediate comment from Paris.

French Defence Minister Gerard Longuet said on Sunday the rebels should not wait for Gadhafi's defeat, while signalling that Paris' objective was that the Libyan leader must leave power eventually.  

Washington said it stood firm in its belief Gadhafi must go.

The messages from two leading members of the Western coalition opposing Gadhafi hinted at the strain the alliance is under after more than three months of air strikes that have cost billions of dollars and failed to produce the swift outcome its backers had expected.

The rebels have refused to hold talks as long as Gadhafi remains in power, a stance which before now none of NATO's major powers has publicly challenged.

"We have ... asked them to speak to each other," Longuet, whose government has until now been among the most hawkish on Libya, said on French television station BFM TV.

"The position of the TNC (rebel Transitional National Council) is very far from other positions. Now, there will be a need to sit around a table," he said.

Asked if it was possible to hold talks if Gadhafi had not stepped down, Longuet said: "He will be in another room in his palace with another title."

Soon after, the State Department in Washington issued a message that gave no hint of compromise.

"The Libyan people will be the ones to decide how this transition takes place, but we stand firm in our belief that Gadhafi cannot remain in power," it said in a written reply to a query.

It also said the United States would continue efforts, as part of the NATO coalition, to protect civilians from attack and said it believed the alliance was helping to up the pressure on Gadhafi.

In an interview published on Monday by the Algerian El Khabar newspaper, Saif al-Islam, a son of the Libyan leader, said his father's administration was in talks with the French government.  

Speaking from Tripoli, the newspaper quoted him as saying: "The truth is that we are negotiating with France and not with the rebels.

"Our envoy to (Nicolas) Sarkozy said that the French president was very clear and told him 'We created the (rebel)council, and without our support, and money, and our weapons, the council would have never existed.

"France said: 'When we reach an agreement with you (Tripoli), we will force the council to cease fire'," he was quoted as saying.

Gadhafi has been holding on to power in the face of rebel attacks trying to break his 41-year rule, NATO air strikes, economic sanctions and the defections of prominent members of his government.

With no imminent end to the conflict in sight, cracks are emerging inside the NATO alliance. Some member states are balking at the burden on their recession-hit finances, and many are frustrated that there has been no decisive breakthrough.

But even countries which support a political solution have not answered the question of how a deal can be hammered out when the rebels and their Western backers say Gadhafi must go while the Libyan leader himself says that is not up for negotiation.

Strains over how to proceed in Libya are likely to surface on Friday when the contact group, which brings together the countries allied against Gadhafi, gathers in Istanbul for its next scheduled meeting.

There was no immediate reaction to the French minister's comments from the rebel leadership at its headquarters in the eastern Libyan city of Benghazi.

LONG MARCH

On the ground, rebel forces trying to march on Tripoli have made modest gains in the past week, but the fighting on Sunday underlined it would be a long slog.

Gadhafi's forces launched a heavy artillery bombardment to try to push back rebel fighters who last week seized the village of Al-Qawalish, 100 km (60 miles) south of Tripoli.

Al-Qawalish is a strategic battleground because if the rebels manage to advance beyond it they will reach the main highway leading north into the capital Tripoli.

A rebel fighter in the village, Amignas Shagruni, told Reuters shells had been landing repeatedly over the past 24 hours from pro-Gadhafi forces positioned a few kilometres to the east. But he said: "No one was hurt, thank God."

During a 20-minute period while Reuters visited the frontline east of Al-Qawalish, at least five shells landed. However, they did not appear to be well targeted.

Libyan state television reported on Sunday that NATO forces had struck an "educational institution" in Tripoli. Jamahiriyah Television quoted a military spokesman as saying there were "human and material" casualties in the air strike in the district of Tajoura, but gave no specific details.

Libya has been convulsed by a civil war since February when thousands of people, inspired by revolutions in neighbouring Egypt and Tunisia, rose up against Gadhafi's rule.

Hundreds of kilometres to the northeast of Al-Qawalish, another force of rebels is trying to push towards Tripoli, though they too are facing tough resistance.

Fighters from the rebel-held city of Misrata, about 200 km(130 miles) east of Tripoli, have fought their way west to the outskirts of Zlitan, the first in a chain of coastal towns blocking their progress towards the capital.

NATO launched its bombing campaign in March after the UN Security Council authorised the use of all necessary means to protect civilians who rose up against Gadhafi.

Gadhafi says the rebels are armed criminals and al Qaeda militants. He has called the NATO operation an act of colonial aggression aimed at stealing Libyan oil.