WASHINGTON—The Obama administration agreed Friday to buy 32 tons of Iran’s heavy water, a key component in atomic-weapons development, a new gambit in a growing White House effort to encourage Tehran to stick to the nuclear agreement reached last year.

The move, immediately criticized by opponents of the original deal, came hours before Secretary of State John Kerry met his Iranian counterpart, Javad Zarif, in New York to try to facilitate Iran’s access to tens of billions of dollars of oil revenues frozen by U.S. sanctions...