A DOJ court filing argues the center faces a "death spiral" without Trump help.
It was not immediately clear how long the construction pause would last.
The Supreme Court has again rejected President Donald Trump's attempt to overturn a $5 million jury verdict in favor of writer E. Jean Carroll.
The president appeared alongside Nassau County Executive Bruce Blakeman, who has he endorsed in the New York governor's race.
Democratic lawmakers are warning about potential conflicts of interest.
During an hourslong meeting that was conducted virtually, the board voted to add Trump's name to the building's facade so it would read "The John F. Kennedy Center for the Performing Arts Restored and Renovated By President Donald J. Trump."