Hassan Rouhani's remarks were seen as part of his efforts to defuse claims by hard-liners that he has given too many concessions to the West in return for too little.
"Without a doubt, nuclear power is our definite right," he said during a ceremony in Tehran marking the 25th anniversary of the death of Ayatollah Ruhollah Khomenei, the founder of the Islamic Republic.
"Resorting to unity and resistance, we will defend interests of Iranian nation," Rouhani said.
Under an interim deal in November, Iran agreed to cap its nuclear activities in return for an easing of sanctions by the West. The U.S. and its allies suspect Tehran is seeking atomic weapons, but Iran denies the charge saying its aims are peaceful.
The next high-level talks aimed at finalizing a deal will be held later this month. Another round of expert-level nuclear talks between Iran and world powers is scheduled for Wednesday in Vienna.
The deal reached by Iran and six world powers the five permanent members of the Security Council plus Germany put limits on Iran's uranium enrichment program in return for the easing of some sanctions. Core sanctions, however, remain in place including measures targeting Iran's oil exports, the pillar of its economy.
Russia's United Nations Ambassador Vitaly Churkin told a news conference in New York that the talks "have been going well but not without problems."
He called for "constructive approaches" by both sides to meet the July 20 deadline for an agreement, adding that one of his "professional ambitions" at the U.N. is to see the Security Council lift four rounds of sanctions imposed on Iran since 2006.
President Rouhani also said Iran would support the fight against terrorism and extremism in the region, a reference to the country's role in helping Syrian President Bashar Assad in his fight against rebels. Assad's government claims those fighting against it are terrorists, not legitimate opponents.
"The Islamic republic of Iran helps those who fight terrorism and extremism in the region," said Rouhani. "Today, Iran is standard-bearer of fighting terrorism and violence in the region."
Iran has been a key regional supporter of Assad in Syria's civil war that pits him against Western-backed rebels seeking his ouster.