The US and French leaders announced on Tuesday that they were working on a "new deal" that would expand and extend the terms of the 2015 accord.
But Mr Rouhani said they had no "right" to renegotiate a seven-party agreement.
He also dismissed US President Donald Trump as a "tradesman" not qualified to comment on global treaties.
"You don't have any background in politics," he said. "You don't have any background in law. You don't have any background on international treaties."
Mr Trump has said the US will reimpose sanctions on Iran suspended under the deal on 12 May unless Congress and European powers fix its "disastrous flaws".
US and European officials are reported to have made progress on two of his demands - for Iran to give international inspectors immediate access to all sites they want to see, and for Iran to halt development and testing of ballistic missiles.
More problematic is his call to remove the deal's time limits, or "sunset clauses", on Iran's sensitive nuclear activities, and make it open-ended.
"Together with a leader of a European country [the Americans] say: 'We want to decide on an agreement reached by seven parties,'" Mr Rouhani said in a televised speech in the city of Tabriz on Wednesday.
"For what? With what right?"
Mr Rouhani said Iran had "shown goodwill to the world" when it signed the accord and had wanted to prove it did "not seek to acquire weapons of mass destruction".
On Tuesday, he warned that there would be "severe consequences" if the US reimposed sanctions. He did not give any details but Iranian officials have said uranium enrichment could be stepped up within days and that the country could withdraw from the Nuclear Non-Proliferation Treaty.