Paris has told the International Olympic Committee "it's now or never" as it bids for the 2024 Olympic and Paralympic Games.
IOC president Thomas Bach last week gave the clearest indication yet that he is in favour of announcing hosts for the next two summer Olympics at September's IOC congress in Lima.
Paris and Los Angeles are competing for 2024 and speculation is growing that Bach wants both to win, so one would become host in 2028.
But Tony Estanguet, IOC member and co-chair of the Paris bid, said the French capital would only be able to host the Games for which it is bidding.
Estanguet, speaking in London on Tuesday, said: "We're okay if the IOC wants to give two Games at the same session in Lima. But on our side, our project is only possible for '24.
"We can't accept '28. It's not possible. It's now or never. Either the IOC family wants to choose Paris for '24 or we will not come back for '28."
Paris lost out to London in a bid to host the 2012 Olympic and Paralympic Games.
The 2016 Olympic and Paralympic Games in Rio were beset by problems and claims of financial mismanagement and corruption.
The 2020 Games in Tokyo have not been immune to crises, either, and with costs spiralling cuts and compromises are being made.
Paris represents a "no risk" option, Estanguet argues.
Budapest, Hamburg and Rome have already left the race for 2024 over domestic concerns about costs.
Paris hosted the second Games in 1900 and again in 1924, but lost out to Barcelona in 1992, Beijing in 2008 and London four years later.
"This is the fourth bid, we learnt a lot," added Estanguet, a three-time Olympic slalom canoe gold medal winner.
"We also believe this is the time to come back to Paris, or to Europe, in '24. We are not against the process, we welcome the process and understand the process, but our project is only possible for '24.
"We cannot imagine hosting the Games in '28. That was not the mandate I received from my team, the political leaders in my country.
"If the IOC can continue with LA and find a solution with LA, that's great. On our side, we cannot imagine to move to '28. We believe we are the best partner for '24. It's a no risk bid."
LA, which hosted the 1984 Games, indicated it is not prepared to back down and switch its priorities to 2028 either.
The LA2024 bid committee said in a statement: "Los Angeles is the right city at this critical time for the Olympic Movement and is only bidding for 2024.
"With all permanent venues already built and 88 per cent public support, only LA 2024 offers the lowest-risk and truly sustainable solution for the future of the Olympic Movement in 2024 and beyond."