Iran said it exceeded a limit on its stockpile of low-enriched uranium set under the 2015 nuclear deal, as it sought to goad Europe, Russia and China into providing relief from U.S. sanctions.

The White House on Monday responded by saying it would keep up what it calls its maximum-pressure campaign until Tehran ends “its nuclear ambitions and its malign behavior.” It further called for a ban on any Iranian uranium enrichment.

President...