He was responding to a statement by US President Donald Trump on Monday that he was willing to meet "any time" with Iran's leaders without preconditions.
Reaction among Trump critics in both parties on Capitol Hill was mixed, with Sen. "I do believe that they will probably end up wanting to meet and I'm ready to meet any time that they want to".
But Trump's remarks did represent a marked softening of tone from a week ago, when he lashed out at Rouhani in a tweet, saying "Never, ever threaten the United States again or you will suffer consequences the likes of which few throughout history have ever suffered before".
'No preconditions, no. If they want to meet, I'll meet anytime they want, anytime they want,' he said.
"There can be no negotiations with the Americans raising the issue of talks from the position of power", he was quoted as saying on the website of the Iranian parliament, calling Trump's decision to pull out of the nuclear deal the "biggest blow to diplomacy".
Heshmatollah Falahatpisheh, the head of influential parliamentary committee on national security and foreign policy, suggested a US return to the nuclear deal, which would bring an end to the economic uncertainty, would be needed before Tehran could think of negotiating.
State Department spokeswoman Heather Nauert told a briefing that Pompeo had said previously that Trump wants to meet with worldwide leaders to solve problems, including with Iranian officials.
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The Cranston Fire in the San Bernardino National Forest has now burned 4,700 acres, destroying 5 homes, and is just 5% contained. Firefighters tried in vain to build containment around the blaze Thursday, but flames kept jumping their lines, he said.
The Trump administration withdrew from the landmark nuclear accord with Iran in May, saying it was too generous to Iran.
White House and administration officials rushed to place caveats on the president's seemingly open invitation.
Asked whether he would set any preconditions for the meetings, he said: "No preconditions, no".
On July 23, US Secretary of State Mike Pompeo said Washington was not afraid to sanction top-ranking leaders of the "nightmare" Iranian regime. Since then, Tehran's clerical establishment has been under increasing US pressure and the prospect of renewed sanctions. 'Good for the country, good for them, good for us and good for the world.
"Based on our bad experiences in negotiations with America and based on United States officials' violation of their commitments, it is natural that we see no value in his proposal", Kamal Kharrazi was quoted as saying by the semi-official Fars news agency.
Economic hardship in Iran forced Khamenei to reluctantly back Rouhani's efforts in securing the 2015 nuclear deal. Yet in meeting with North Korea's Kim Jong-un and Russian President Vladimir Putin, Trump has taken bold steps to ensure regional and even global peace. We got our prisoners back.