TEHRAN—Iran’s conservatives received a landslide in the country’s parliamentary elections, strengthening hard-liners opposed to diplomacy with the West. But a history-small turnout dealt a community rebuke to the establishment’s phone for unity in the face of escalating tensions with the U.S.

Acknowledging the defeat of nonconservative factions, the moderate President Hassan Rouhani on Sunday termed on the new lawmakers to stand for not just all those who voted but all Iranians.