Iran’s central bank governor, in a rare visit to Washington, demanded the Obama administration take more steps to facilitate his country’s banking transactions world-wide and warned the landmark nuclear agreement reached last year could be at risk if the U.S. doesn’t act.

Iranian banks have been unable to process international money transfers and finance trade freely in the months since the deal went into effect in January. Iran also has faced obstacles in repatriating tens of billions of dollars of its oil revenues that were...