The warning came as Trump leaves a trail of destruction in Washington, demolishing the White House East Wing to make way for a $600m ballroom and ordering a renovation of the Lincoln Memorial reflecting pool that resulted in algae blooms and a peeling liner.

The court filing represented the first time that Trump’s allies have raised the prospect of knocking down the Kennedy Center – a 100ft-high complex with a concert hall, opera house and theatre – as the dire alternative to closing it for two years of improvements. Such an aggressive move would be sure to face legal challenges, protests and an outcry from historic preservation groups.

The threat emerged on Monday as the administration urged a federal judge to reject a fresh legal challenge to Trump’s efforts to put his name on the Kennedy Center. The dispute has become part of a months-long battle over the president’s attempt to alter the memorial created by Congress in honour of John F Kennedy, the 35th US president who was assassinated in 1963.