The White House moved to shield former counsel Don McGahn from testifying before Congress, asserting a broad immunity to compelled testimony as Democrats investigate President Donald Trump’s efforts to curb Special Counsel Robert Mueller’s Russia probe.

“Because of this constitutional immunity, and in order to protect the prerogatives of the Office of the Presidency, the president has directed Mr. McGahn not to appear at the committee’s scheduled hearing on Tuesday, May 21, 2019,” White House Counsel Pat Cipollone wrote May...