WASHINGTON — President Obama and Secretary of State John Kerry have a simple explanation for their surprising success in getting Iran to dismantle much of its nuclear infrastructure, ship out 98 percent of its nuclear fuel and release five American prisoners: Patient diplomacy, backed by escalating economic sanctions, accomplished more than military action ever could have.

Iran’s top nuclear negotiator was heading back to Tehran on Sunday to consult with his nation’s leadership, as negotiators remained divided over how to limit and monitor Tehran’s nuclear program and even on how to interpret the preliminary agreement they reached two months ago.