GENEVA — Speaking in English and using PowerPoint, Iran’s foreign minister outlined a proposal to representatives of the big powers on Tuesday that would constrain his country’s nuclear program in return for a right to enrich uranium and an easing of the sanctions that have been battering the Iranian economy.

After the discussions, Iran’s deputy foreign minister, Abbas Araqchi, and his team met for about an hour at the United Nations headquarters here with the American delegation, led by Wendy Sherman, a senior State Department official. The substance was not disclosed, but the meeting itself was unusual.

The proposal presented by the foreign minister, Mohammad Javad Zarif, at negotiations on Iran’s disputed nuclear program, called for “an end to an unnecessary crisis and a start for new horizons,” according to Iranian officials.

In a possible sign that the negotiations have turned serious after years of delay and obfuscations, a senior State Department official suggested that the discussions had been workmanlike.