"President-elect Trump spoke with IOC President Bach to express his strong support for the @Olympics & #LA2024's plans to host a great games," LA 2024 revealed on Twitter.
An IOC spokesman later confirmed the call had taken place but did not provide details of the conversation.
The call follows assurances from Garcetti that Trump's election as US president will not harm Los Angeles' bid for the games.
There has been speculation that Los Angeles' hopes could be hurt by the election of Trump, who won the race for the White House after a campaign characterised by rhetoric which included a call for a temporary ban on Muslims travelling to America and describing illegal Mexican immigrants as rapists and drug-traffickers.
Los Angeles, Paris and Budapest are the three cities vying for the right to stage the 2024 Games.
The IOC will make its final decision in September 2017 at a meeting in Lima.
Los Angeles previously hosted the Olympics in 1932 and 1984.
If it wins, Los Angeles will be the first American city to host the Summer Olympics since Atlanta in 1996.