European diplomats warned Monday that Iran is preparing to abandon parts of a landmark nuclear deal in response to new U.S. sanctions, a step that risks inflaming tensions after the Trump administration dispatched warships to the Persian Gulf to deter potential Iranian attacks.

A senior European diplomat said Iranian officials have been considering a partial withdrawal from some parts of the multination accord that placed strict but temporary limits on a broad swath of Iran’s nuclear work. Such a step may include stepping...