WASHINGTON—The Trump administration’s decision last week to pull out of the nuclear deal with Iran will create an economic policy challenge for the U.S.: How does it enforce sanctions that the rest of the world no longer backs?

The White House last week announced a plan to reimpose economywide sanctions on Iran in two stages over six months, banning any financial or business dealings with blacklisted entities. Any non-Iranian bank, firm or person who violates that ban risks penalties themselves, including the possibility of...