Rouhani said the Iranian people and their government will "spare no effort" in supporting the nation.
Western governments have tightened the sanctions pressure on Iran as punishment for a controversial nuclear program. The United States and its allies suspect Iran is trying to develop a nuclear weapon, an allegation the Iranian government denies.
Rouhani, a former nuclear negotiator, said his adversaries have so far been unable to cripple Iran's general ambitions.
"Since the early stages of the Islamic Revolution, the enemies have failed to bring the Iranian nation to its knees," he was quoted by the semiofficial Fars News Agency as saying.
U.S. State Department spokeswoman Jen Psaki told reporters Wednesday nuclear issues would be on the table during bilateral defense talks with Russian officials in Washington.
"They agree and share a concern about the ongoing threat of nuclear weapons from Iran and from North Korea," she said.
Iranian officials said they'd be willing to discuss the nuclear issue with the European Union if sanctions pressure eases. Two rounds of multilateral talks this year produced few results.