WASHINGTON — It should have been Scott Pruitt’s finest moment.

Mr. Pruitt, the chief of the Environmental Protection Agency, has sought to make his name as the Trump administration’s most effective eraser of regulations on American industry. On Tuesday, he formally announced his most sweeping regulatory rollback to date: a plan to weaken President Barack Obama’s stringent rules on planet-warming tailpipe emissions.

Mr. Pruitt’s proposal is designed to unravel a signature piece of Mr. Obama’s environmental legacy, hand a victory to the American automakers and please his boss, President Trump. But instead of basking in glory, Mr. Pruitt is caught up in a swirl of allegations of impropriety — most recently centered on the fact that last year he rented a room in Washington from the wife of a prominent lobbyist.

Mr. Pruitt unveiled his rollback in a hastily announced presentation at E.P.A. headquarters after canceling a plan to speak at a suburban Virginia auto dealership, a more public setting that might have exposed him to questions about the lease arrangement, or about his first-class air travel at taxpayer expense over the past year, for which he has also faced criticism. Mr. Pruitt declined to field questions at the event.

Late Monday, Mr. Trump phoned Mr. Pruitt to reassure him that his job was safe. “Keep your head up, keep fighting, we got your back,” Mr. Trump told Mr. Pruitt, according to an administration official. Then on Tuesday morning, John F. Kelly, the White House chief of staff, called Mr. Pruitt to reaffirm the president’s sentiment, the official said.