Asian companies that had provided a lifeline to Iran after the U.S. reimposed sanctions last year are pulling back, hurting the hobbled Iranian economy and leaving the Islamic Republic with less incentive to stay committed to a multination nuclear deal, Western diplomats say.

The companies are reacting to the Trump administration’s moves this month to squeeze Iran’s oil exports and impose a terror designation on its paramilitary force. Among Asian businesses rethinking their dealings with Iran are banks, oil companies and...