But both sides said any tie-up would depend on certain conditions being met first, as time runs out for indebted Alitalia.

Italy's government and Alitalia shareholders have been betting on Air France-KLM raising its stake from 25 percent and possibly even taking control of the company.

But there are disagreements over financial commitments and a possible business strategy for the Italian group should a merger go ahead, sources familiar with the matter said.

"Our conditions for helping Alitalia are very strict. If the conditions are met, I am ready to go ahead," Air France-KLM Chief Executive Alexandre de Juniac told French daily Les Echos on Tuesday, without giving more details on the terms he had in mind.

Gilberto Benetton, who invests in Alitalia via motorway group Atlantia's 8.9 percent stake in the airline, said earlier on Tuesday he would welcome Air France-KLM taking control of the group, but warned Italy's interests should be protected first.

Italian Prime Minister Enrico Letta, other ministers, banks and Alitalia's management met on Tuesday to find a way of beefing up Alitalia's finances to give it greater negotiating clout in its dealings with Air France-KLM.

But the talks failed to reach any decision because of the uncertain political climate and another meeting was called for next week.

There are worries that any Air France-KLM investment would clash with Italy's ambition to make Rome a hub for intercontinental flights, and instead turn Alitalia into a regional player and trigger job cuts.

But de Juniac's comments signaled he did not doubt Alitalia's ability to operate on long-haul routes - a strategy the group is betting on to revive its fortunes after its plans to become a strong regional player came unstuck in the face of tough competition and lower demand.

"Air France-KLM-Alitalia, if one day we are united, could become a very great European brand. In such a scenario, we could supply (Alitalia's) long-haul flights with passengers from Air France and KLM and they could do the same for us," he said.

De Juniac added that he could see Alitalia boosting its intercontinental routes where its own network might be weak.

"Alitalia has strong points in Africa, Latin America and North America, where there is a strong Italian diaspora that can complement ours," he told the paper.

"Alitalia strengthens our commercial footprint pretty much everywhere. There are already many synergies."

NO CAPITAL INCREASE

Analysts said Air France-KLM was unlikely to give up on Alitalia by letting it fail and opening Europe's fourth-largest travel market to more competition.

But Air France-KLM has set strict conditions on how the company should be restructured. Sources said last week that Air France had voted against a proposed capital increase at Alitalia of at least 100 million euros ($135 million).

"Air France-KLM voted against the capital increase because the proposals on how to revive Alitalia were inexistent," a banking source said. "The conditions have no chance of being met."

In the absence of other bidders, Italy's bargaining power is seen as limited. The Alitalia board was informed last week of possible interest from China, Russia and the United Arab Emirates, but Benetton said there was nothing concrete.

Alitalia's board is due to meet again on Thursday to decide how to source the funding needed to keep the company afloat.

Analysts said the airline required an injection of about 500 million euros to keep going and be able to invest in a strategy focused on the more lucrative long-haul market.

Last week the company said its liquidity stood at 128 million euros after reporting another heavy first-half loss. ($1 = 0.7393 euros)

(Additional reporting by Alberto Sisto and Steve Scherer in Rome and Matthias Blamont in Paris; editing by Tom Pfeiffer)

By Agnieszka Flak and Lionel Laurent