Paris and Los Angeles say they are only interested in hosting the 2024 Olympics and Paralympics – and not the 2028 Games.
There have been suggestions the International Olympic Committee may award both the 2024 and 2028 Games in September.
“2024 is now or never for us,” co-chair Tony Estanguet told BBC Sport.
The LA 2024 committee later issued a statement saying their bid represents “the right city at this critical time”.
The American city’s statement added: “With all permanent venues already built and 88% public support, only LA 2024 offers the lowest-risk and truly sustainable solution for the future of the Olympic movement in 2024 and beyond.”
The 2024 Games are scheduled to be awarded at September’s IOC summit in Lima, Peru, with Paris the favourite to win.
“We believe we have the strongest offer but it is only available for 2024,” added Estanguet. “We can’t host the Games in 2028 because we don’t have the project available for 2028.
“We have the guarantees, we have the public support, we have the political support, we have 95% of existing venues. This is the fourth bid from Paris and 2024 is the centenary of the Games in Paris.”
There have been reports the losers of the 2024 bid could be awarded the following Games in 2028.
“All options are on the table, and this includes also the 2024-2028 procedure and vote,” said IOC president Thomas Bach last week.
Estanguet, a three-time Olympic canoeing champion, says the bid committee has been in discussions with the IOC since the beginning of the bidding process.
He added that the bid committee has talked through the issue of 2028 with the IOC on several occasions.
Earlier this week, Eric Garcetti, the mayor of LA, warned the Americans were intent on winning the right to host the 2024 Games.
“We are competing for 2024,” he told insidethegames. “Full stop. We have never contemplated anything else.”