Two more musicians have cancelled shows at the Kennedy Center, after its board voted to rename the venue to include US President Donald Trump's name.

The Cookers, a veteran jazz band, said they cancelled two New Year's Eve shows. In a statement, the group did not mention Trump or the Kennedy Center, but said the decision had "come together very quickly".

Another group, Doug Varone and Dancers, said they would not perform two shows scheduled for April because of the name change, adding: "We can no longer permit ourselves nor ask our audiences to step inside this once great institution."

Richard Grenell, the Kennedy Center's president, called the cancellations "a form of derangement syndrome".

He said that the artists cancelling shows "were booked by the previous far left leadership".

"Their actions prove that the previous team was more concerned about booking far left political activists rather than artists willing to perform for everyone regardless of their political beliefs," he added.

Announcing their decision to cancel, the Cookers said: "Jazz was born from struggle and from a relentless insistence on freedom: freedom of thought, of expression, and of the full human voice."

"We are not turning away from our audience, and do want to make sure that when we do return to the bandstand, the room is able to celebrate the full presence of the music and everyone in it," they added.

Billy Hart, the band's drummer, told the New York Times the name change "evidently" played a role in the decision to cancel.

Kristy Lee, a folk singer, also recently said she was cancelling her January show.

"When American history starts getting treated like something you can ban, erase, rename, or rebrand for somebody else's ego, I can't stand on that stage and sleep right at night," Lee said in a social media post.

Last week, musician Chuck Redd called off his Christmas Eve performance, which he has hosted annually since 2006, citing the centre's name change.

Grenell demanded $1m (£740,000) in damages from Redd, and said the cancellation was a "political stunt" that "has cost us considerably".

The Kennedy Center's board, which Trump filled with allies, voted earlier this month to rename the institution the Donald J Trump and the John F Kennedy Memorial Center for the Performing Arts. New signage was added the building's exterior the next day.

Some US lawmakers and legal scholars argued that because the centre was named in a 1964 law, Congress must vote to make the name change official.

Some members of President John Kennedy's family have denounced the move. The centre was named in Kennedy's memory shortly after he was assassinated.

Joe Kennedy III, a former House member and grandnephew of the late president, said the venue "is a living memorial to a fallen president and named for President Kennedy by federal law".

"It can no sooner be renamed than can someone rename the Lincoln Memorial, no matter what anyone says," he added.