* Paris, Los Angeles are only bidders for 2024
* IOC to seek three-way deal before vote in September (Updates with new quotes)
By Karolos Grohmann and Brian Homewood
LAUSANNE, Switzerland, July 11 (Reuters) - The International Olympic Committee (IOC) on Tuesday moved close to an agreement that will allow Paris and Los Angeles to each host the Summer Games between now and 2028 and rule out any other cities from bidding.
The two cities were the only ones left in the race to stage the 2024 Games and an IOC session voted that it would seek a "tri-partite agreement" for one host in 2024 and the other in 2028.
The original plan had been to choose one for 2024 at the next session in Lima on Sept. 13, discard the other and start a whole new bidding process for 2028.
For the agreement to work, either one or both cities would have to be willing to accept the 2028 Games if they were not awarded 2024, the IOC said.
The mayors of both cities said they would work towards reaching an agreement while IOC president Thomas Bach said he believed a deal could be struck by August.
"We will start right away," Bach told a news conference. "There are procedures to be followed in the two cities but I hope in August we could be there if everything goes well."
Bach said the decision would "ensure the stability of the Olympic Games for 11 years (which) is really, in our world, something extraordinary." He described it as a "win-win-win" situation.
Should there be no three-way agreement, the vote at the Lima session will be a straightforward selection of only the 2024 host city.
Los Angeles mayor Eric Garcetti, whose city hosted the Games in 1932 and 1984, said the decision was a welcome departure from what he described as the traditional "winner-takes-all" process.
"I'm sitting up here with two mayors of two cities which will host, after Tokyo (in 2020), the next two Olympics ... We are one step closer to making that happen and I have full confidence we will get there," he said.
His Paris counterpart Anne Hidalgo, describing the process as historic, said she was committed to reaching an agreement so "Paris can get back to this wonderful adventure that it has been waiting for for 100 years."
Paris, which hosted the 1900 and 1924 Games, failed with bids to host the 1992, 2008 and 2012 Olympics.
The IOC has been desperate to overhaul its bidding process after four cities - Hamburg, Rome, Budapest and Boston - pulled out of the 2024 race, scared off by the size, cost and complexity of hosting the Games.
Hidalgo said Paris had "reflected long and hard about embarking once again on this candidature."
Before the vote on Tuesday, Paris and Los Angeles presented their bids to the 83 IOC members present, with the French capital receiving a major boost from the presence of President Emmanuel Macron, who addressed the session.
United States president Donald Trump did not attend but later tweeted his support for Los Angeles. "Working hard to get the Olympics for the United States (L.A.). Stay tuned!," he said. (Editing by Ed Osmond and Ken Ferris)