TEHRAN — Dozens of protesters hurled eggs and at least one shoe at President Hassan Rouhani as he returned to Tehran on Saturday after a groundbreaking phone call with President Obama and other outreach to the West at an annual gathering of world leaders at the United Nations.

The protest — coming even as supporters gathered at the airport to cheer his diplomatic outreach — quickly laid bare the political fissures in Iran over whether to engage with the United States, and the challenges Mr. Rouhani and his aides face as they try to have international sanctions over the country’s nuclear program lifted.

Mr. Rouhani was standing in his car, waving through the sunroof as he passed supporters when opponents began to pelt the vehicle. Security guards scrambled to shield the president with an umbrella as other protesters blocked the road by praying on the pavement.

“Long live Rouhani, man of change!” the president’s backers shouted, as a small police contingent struggled to control the crowd of about 200 that seemed mostly to be Rouhani supporters. The hard-liners responded by shouting, “Our people are awake and hate America!”