(Updates with Macron comments)
By Karolos Grohmann and Brian Homewood
LAUSANNE, Switzerland, July 10 (Reuters) - French President Emmanuel Macron expressed "pride, humility and determination" and Los Angeles Mayor Eric Garcetti spoke of his city's proud Olympic past as the rivals to host the 2024 Games met International Olympic Committee President Thomas Bach on Monday.
The IOC will hold a meeting on Tuesday where it is expected to ratify an executive board recommendation to award both the 2024 and the 2028 Games at the same time, ensuring both candidates host one Games.
However, the IOC would still have to decide who goes first, and the two candidates are lobbying intensely to try to get the 2024 Games they originally bid for.
Macron's presence on Tuesday is an unusual move. Heads of state generally turn up only for the host city vote, which this year will take place in Lima, Peru, on Sept. 13.
Garcetti, whose city hosted the 1932 and 1984 Games, supported the IOC's decision to award both editions at the same time.
"We welcome the decision to look at simultaneous awarding of two summer Games," he said after meeting the IOC's Bach at the Olympic museum.
"We are very excited even in that context to share our unique story with the IOC members, the soul of LA, the taste of the city. We have been a transformative partner every time we had the Games."
Paris is also hoping to stage the Games for a third time, having previously hosted in 1900 and 1924, and Macron said he came with "a sense of pride, determination and humility".
"I came here for two things: pride, for the candidature and being part of this win-win-win situation, and also to carry the values of Olympism the world over. I support them fully," Macron said.
"We need multilateralism, the structures that provide agreement among nations ... and tolerance, which the Olympic movement illustrates well."
Paris has already failed in three attempts to land the Olympics, in 1992, 2008 and 2012.
"A unique team in France set up this project," Macron said. He had already met with the IOC two days after being elected in May.
"The project was built by a team, the national Olympic committee, the city of Paris, and is marked by the complete unity behind this project."
Bach, whose meeting with Macron lasted close to an hour and a half compared with 40 minutes for the mayor of Los Angeles, said a decision to give the green light on a double allocation would "create a win-win-win situation for LA, Paris and the entire Olympic movement."
Paris is seen as the frontrunner in the race for the 2024 Games, with Los Angeles having hinted they would accept the Games for 2028.
Four other cities -- Hamburg, Rome, Budapest and Boston -- were in the running for the 2024 Games before dropping out over cost and size concerns, forcing the IOC to overhaul the bidding with the double awarding to make it more attractive to potential hosts of the Games. (Reporting by Karolos Grohmann; writing by Brian Homewood; editing by Larry King)