Hassan Rowhani on Monday said the United States must recognise all the rights of the Islamic republic, including its nuclear rights, in his first press conference since being elected Iran's new president.
"Any dialogue with the United States must be based on equality and mutual respect and on conditions. The US should not interfere in our internal affairs, recognise the rights of Iran including nuclear rights and stop its unilateral policies and pressure," the cleric said.
"The next (Iranian) government will not give up the legitimate rights of the country."
The United States, Israel and the West suspect Iran's nuclear programme is aimed at developing weapons, while Iran insists it is for peaceful purposes such as generating electricity and producing medical isotopes.
The White House on Saturday said Washington is prepared to engage Iran directly over its nuclear programme with a view to reach a "diplomatic solution" to the controversy.
Diplomatic ties between Iran and the United States have been cut since the 1979 Islamic revolution when Iranian Islamist students took over the US embassy.
Rowhani was on Saturday declared winner of Iran's presidential election, ending Mahmoud Ahmadinejad's eight-year term during which relations between Washington and Tehran deteriorated further.