Trump on Friday said on social media he instructed the Commerce Department to "make all necessary arrangements with Congress to allow a full and complete transfer of this Institution" and give lawmakers responsibility over its operation, maintenance and management.
It was not immediately clear how Trump's directive could be carried out. The Kennedy Center was created by Congress in 1958 and is run by a board of trustees that the president has packed with allies in his second term.
Trump's announcement came after a judge on Friday ruled the performing arts centre, which Trump renamed the Trump Kennedy Center, cannot be renamed without an act of Congress.
District Judge Christopher Cooper in Washington directed the Trump administration to take down all physical signage bearing Trump's name and to eliminate any references to a Trump Kennedy Center from official materials within 14 days.
"The Kennedy Center's organic statute makes crystal clear that the center is to be named for President Kennedy, and it cannot bear any other formal name or public memorial based on the Board's unilateral say-so," Cooper wrote.
"Congress gave the Kennedy Center its name, and only Congress can change it."
Cooper's order also stopped the Trump administration's planned two-year closure of the Kennedy Center for major renovations, though the judge said "sorely needed" repairs to the aging building could move forward.
The judge said his decision "does not purport to dictate how the centre should be run, nor does it prescribe any particular plan for the institution — construction, closure, or otherwise — moving forward."
In a Friday post on Truth Social, Trump said large-scale renovations set to begin in June would be impossible without a closure and that Cooper's order to keep the Centre open would be dangerous.
"I cannot be involved with a situation where danger to the Public is allowed to flourish in plain and open sight," Trump said.
Trump's plan to renovate the Centre is part of a broader push by the Republican leader to reshape Washington's monumental core. He also intends to erect a 76-metre arch and to build a 8300sq m ballroom at the site of the demolished East Wing of the White House.
Those efforts also face court challenges. A federal appeals court has allowed the Trump administration to move ahead with building the ballroom as it considers a lawsuit seeking to block it.
"This is a powerful blow against the Trump administration's corruption," lawyers Norm Eisen and Nathaniel Zelinsky said.
The board could still close the Kennedy Center, Cooper wrote, "should it come to this decision anew after independently balancing its multiple obligations to the Center in a prudent fashion."
The Kennedy Center opened in 1971 as a living memorial to the late President John F Kennedy.
with AP