If the diplomacy fails, "It won't be the end of the world," Zarif told the New Yorker.
But in that case, "The US will have lost a major opportunity, probably unique," Iran's top diplomat added.
"But, for us, our population is accustomed to making necessary sacrifices to preserve its dignity and its rights.
"It's not about nationalism or chauvinism. It’s simply about having historical depth. Several years are a brief period in the history of a country with millennia as its depth."
Zarif's comments come as Iran and the Group 5+1 (Russia, China, the US, Britain, France and Germany) continue negotiating to hammer out a lasting accord that would end more than a decade of impasse over Tehran's civilian nuclear program.
Iran's foreign minister, who is in Luxembourg, on Monday met his counterparts from Britain, France and Germany.
He said the meetings were aimed at discussing "how to expedite the talks in the few tough days ahead."
Meanwhile, the Iranian parliament on Tuesday approved the details of a bill requiring the government to safeguard the country's nuclear rights in a possible deal with the five permanent members of the UN Security Council – the United States, Britain, China, France and Russia – plus Germany.
During an open session of the parliament, the bill was approved with 213 votes in favor, 10 against and five abstentions. It demands that the total removal of anti-Iran sanctions be included in the text of any final nuclear agreement with the six countries, and urges the lifting of all sanctions imposed on Iran on the same day that the Islamic Republic starts to fulfill its obligations under a final accord.