In a statement, Jamie, Alexander and Nina Bernstein said their father had a "nice, big nose" and they feared attempts were being made to bring Cooper "down a notch".

They added: "Bradley chose to use makeup to amplify his resemblance, and we're perfectly fine with that.

"We're also certain that our dad would have been fine with it as well."

Their statement added that Cooper "included the three of us along every step of his amazing journey as he made his film about our father".

"We feel so fortunate to have had this experience with Bradley, and we can't wait for the world to see his creation."

In Maestro, Cooper stars opposite Carey Mulligan in a drama that focuses on Bernstein's relationship with his wife, Felicia Montealegre.

Bernstein wrote the music for West Side Story and won 16 Grammy Awards over the course of his career. He died in 1990.

But an official trailer for Maestro caused a stir after Cooper was seen with a notably larger nose than his real one.

Jewish actress Tracy-Ann Oberman claimed this was the equivalent of black-face or yellow-face.

She wrote on Instagram that if Cooper was chosen over a "Jewish A-lister who can equally play that role" then his acting should be "so magnificent and truthful that the character of Bernstein shines through what he already looks like".

Oberman is not alone in criticising the casting of Cooper. Daniel Fienberg, chief television critic with The Hollywood Reporter, tweeted earlier this year that it was "problematic".

There have also been objections to Cillian Murphy, who is not Jewish, playing the Jewish nuclear physicist Robert Oppenheimer.

David Baddiel has described such casting as "complacent" and linked to "Jewish erasure".

However, journalist and tech entrepreneur Brian Krassenstein said he was fine with Cooper playing Bernstein.

He posted on X, formerly known as Twitter: "Relax! Movies are art. An actor's job is to portray the character they play to the best of their ability.

"I'm Jewish. My nose is large. Many Jewish people's noses are large. It's just a fact."