Tehran and six world powers, including the United States, agreed to the deal in July when Iran promised to scale down its nuclear activities in return for the lifting of painful UN and Western sanctions, including on its lifeblood oil exports.
"Every year as president I've taken this opportunity, the hope of spring, to speak directly with the people of Iran about how we might open a new window and begin a new relationship with our countries," Obama said Saturday in a video message to the Iranian people, posted online one day ahead of Nowruz.
"Now, for the first time in decades, there's a chance for a different future."
The Nowruz holiday comes just two months after implementation of the deal began.
Throughout the 12-year standoff that preceded the agreement, Iran always denied wanting nuclear weapons, saying its nuclear activities were exclusively for peaceful purposes such as power generation.
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"The nuclear deal was never intended to resolve all the disputes between our two nations, and the United States continues to have profound differences with the Iranian government," Obama said.
"But even as our two governments continue to have serious disagreements, the fact that we are now talking to each other on a regular basis, for the first time in decades, gives us an opportunity, a window, to resolve other issues."
"As we do, I firmly believe we can continue to expand the connections between the American and Iranian people," Obama added.
Washington cut diplomatic ties with Iran in 1979, when its embassy in Tehran was stormed by students, months after the Islamic revolution, leading to a 444-day hostage crisis.
Obama will help bury the hatchet in a separate diplomatic dispute on Sunday when he arrives in Cuba after a more than half-century-long Cold War conflict that turned the communist island and its giant neighbor into bitter enemies.
"My visit will be a reminder that even after decades of mistrust it is possible for old adversaries to start down a new path," Obama said.
"As you and your families welcome the new spring this Nowruz, I wish you a happy, healthy and prosperous new year, and I hope that the friendship and ties between the American and Iranian people will continue to grow," he added.