The decision came after a meeting in which a lawyer for the billionaire, Gautam Adani, made an unusual offer, according to people familiar with the matter.
Though illicit e-cigarettes have flooded in from China, the new policy could allow major tobacco companies to sell from prime shelf space at thousands of stores.
Republicans put down a right-wing revolt to push the measure through the House, but it faces changes in the Senate that could delay its final passage past a Friday expiration.
A Republican, Mr. Kempthorne rose to prominence as the mayor of Boise in the late 1980s and early ’90s, as the city became a haven for outdoor enthusiasts.
Our reporter was with President Trump at the White House correspondents’ dinner when a gunman breached security. He describes the frantic scenes that unfolded.