WASHINGTON—The White House is pushing to ease the way for companies to complete deals with Iran, aiming to cement the landmark nuclear agreement reached last year and make it difficult for future administrations to undo it, senior U.S. officials said.

The effort, which borrows from President Barack Obama’s playbook for solidifying U.S. relations with Cuba, got a boost this week when Boeing Co. reached a $17.6-billion deal with Iran to sell commercial jets to the country’s main airline.

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