The decision by the board, which is chaired by Trump and composed of his allies, came less than two hours after a federal judge blocked the centre from adding Trump's name to its facade for the second time in five months.
In a social media post, Trump said the renovation work would not start until an appeals court weighs in on the judge's order.
"If the ruling is a negative one, which it should not be, and is not overturned by the US Supreme Court, the Reconstruction and the Renovation of The Kennedy Center will not take place," he wrote on his Truth Social platform.
Tuesday's developments were the latest twists in the saga of the John F. Kennedy Memorial Center for the Performing Arts since Trump regained the White House, named himself chairman of the centre's board and announced plans to reshape its programming.
The centre, which is also a memorial to the assassinated Kennedy, opened in 1971 with the world premiere of Leonard Bernstein's requiem mass for Kennedy. It has over the decades been home to the Washington National Opera and the National Symphony Orchestra and hosted such performers as Mikhail Baryshnikov and Wynton Marsalis. It also hosts the annual Kennedy Center Honors, recognising the lifetime of achievement of leading artists.
In response to Trump's takeover, artists have cancelled performances in protest, and the opera and the symphony were forced to find other venues, while revenue cratered.
The board has warned the centre's finances are so shaky that it may soon not be able to honour payroll obligations or maintenance contracts.
Trump's campaign to remake the centre is part of his broader effort to leave his cultural and aesthetic mark on the US capital, including a large new ballroom to replace the White House East Wing he ordered demolished, a troubled renovation of the Lincoln Memorial Reflecting Pool and a planned "triumphal arch" near the nation's main cemetery honouring its war dead.
The centre's board has said the venue is in dire need of immediate repairs.
US District Judge Christopher Cooper in Washington issued an order on Tuesday temporarily halting the centre's latest proposal to put Trump's name on the building. The centre was named for Kennedy as a memorial under a law signed by President Lyndon Johnson after his assassination.
In addition, Cooper said the board cannot proceed with plans to rename the campus where it sits the "President Donald J. Trump Plaza."
"Simply put, defendants cannot install memorials for President Trump or anyone or anything else at the Kennedy Center without Congress' blessing," he wrote.
Like Trump, the board has argued that adding his name in honour of his efforts is necessary to ensure his continued commitment to its survival.
Trump said on social media that the Justice Department, which represents the centre, will appeal the order.
