President Barack Obama sent his Iranian counterpart a letter saying Washington was "ready to resolve the nuclear issue" with Iran.
Iran is suspected of pursuing the technology needed to manufacture a nuclear weapon. Rouhani repeated in an NBC interview Iran's long-time claim the country's nuclear program is meant for peaceful purposes.
Ayatollah Sadeq Amoli Larijani, Iran's top judicial official, said Washington has a double standard when it comes to nuclear and chemical weapons. He noted the United States was the only country to use a nuclear weapon in war and had the largest stockpile of such weapons.
"The Islamic Republic does not seek nuclear weapons, not because of U.S. threats or claims, but because we have religious standards in our defense and military affairs," he was quoted by state-funded broadcaster Press TV as saying Thursday.
The White House said there are no plans for a presidential meeting on the sidelines of next week's annual meeting of the U.N. General Assembly.
The International Atomic Energy Agency last week said it suspected there may be a military dimension to certain aspects of Iran's nuclear program.