GOP congressional leaders have stood aside the past four months as President Donald Trump has attacked legislative branch prerogatives — shuttering agencies, canceling federal grants and imposing sweeping tariffs.

WASHINGTON—The Library of Congress—long a sleepy, noncontroversial staple of the nation’s capital—has become the latest battleground in President Trump’s power struggle between the branches of government.

Lawmakers are raising separation-of-powers concerns as the White House seeks to install a Justice Department official at the legislative-branch institution.