The Rolling Stones are not the only musicians to protest against unauthorized use of their music for political campaigning. He has used their song before, which led to the group complaining about it in 2016 before he was elected president.
The statement emphasized that if Trump continued playing their music, he would be subject to legal action. The band says Trump's campaign has ignored previous cease-and-desist orders.
It was initially played at Republican party primaries.
The BMI added that it has not yet received any response from lawyers acting for Trump.
The Stones are not the first major act to call on the president to stop using their songs.
Donald Trump has used the song You Can't Always Get What You Want since his 2016 campaign
As these disputes have arisen, at issue is whether a song's use in a campaign rally is covered by a blanket license held by the host venue for all performance purposes.
News of the Stones taking up the fight to have their song excluded from campaign appearances follows on the heels of the Tom Petty family uniting last weekend to release a statement objecting to "I Won't Back Down" at the president's contentious campaign rally in Tulsa.
The same song was used by the Trump campaign during the 2016 USA election.
Pharrell Williams, Rihanna, Aerosmith, Adele, Neil Young and the estate of singer Prince have all hit out after the use of songs by Trump.
Buckley sang the song in the original Broadway production of Cats in the early 1980s. But in a Twitter Q&A that year, Mick Jagger also admitted that the band were stuck in their predicament: "When you appear in America ...if you're in a public place like Madison Square Garden or a theater, you can play any music you want, and you can't be stopped".
The Rolling Stones are not the only artists who don't want to be associated with the US President.