PARIS (CNN) -- With the World Cup looming just days away, negotiations to end a crippling Air France strike were suspended Saturday morning when representatives of the main pilots' union abruptly left the bargaining table.

The French government responded to the breakdown by saying it may soon intervene.

"It is not the World Cup which worries me. What worries us ... is the future of Air France," Prime Minister Lionel Jospin said. "I believe everyone must be worried about this and for that reason if the government can be useful ... we will play a role in the hours that come."

Following marathon overnight discussions, the president of the main pilots' union said talks to end the six-day-old strike broke off without agreement and would resume Monday, only two days before the June 10 kickoff of the World Cup in Paris.

"Last night we lost an enormous amount of time. The management of Air France has still not understood that pilots are determined," said Jean-Charles Corbet, president of SNPL, the main union.

The airline has yet to comment on Saturday's development.

Pilots have demanded that management drop plans to cut their salaries. The state-controlled airline wants to save $84.1 million, or 500 million francs a year, for three years from pilots' wages as part of a massive budget-overhaul plan. In exchange for the pay cut, Air France has offered the striking pilots a slice of the company's share capital, but the pilots have so far rejected the offer.

"We gave the chairman of Air France a program destined to make pilots his partners and we are waiting to hear his response to this program," Corbet said. "If the chairman does not want look at this program, there will be grave decisions to take."

The dispute has forced Air France -- an official World Cup sponsor -- to cancel the vast majority of its flights since last Monday and it has announced a skeleton service for the weekend, casting a shadow over the start of the World Cup -- set to begin June 10 in Paris.

The strike has already cost Air France an estimated $100 million, a total increasing at a rate of $16.9 million a day as the strike drags on.

France's leftist government has accused the pilots of holding the World Cup hostage and has firmly backed Air France directors in their push to cut a hefty salary bill in a bid to fund an ambitious investment program.

The company has promised to provide flights for all 32 teams taking part in the World Cup.