Britain, China, France, Germany, and Russia -- dubbed the "4+1" -- are struggling to save the accord after the United States withdrew from it in 2018.

Washington unilaterally reimposed sanctions on the Islamic republic.

Iran has stepped up its nuclear activities in the past year in retaliation for Washington's pullout from the deal, officially known as the Joint Comprehensive Plan of Action, or JCPOA.

"Fortunately, yesterday in Vienna, the 4+1 clearly stated that they stand by the JCPOA and that America does not have the right to misuse it," Rouhani said in remarks to the weekly cabinet meeting broadcast on state television.

"They have not only pulled out of the JCPOA but also punished whoever has abided by it."

Rouhani called Washington's drive to reimpose UN sanctions against Iran "futile and childish."

European Union senior official Helga Schmid, who chaired the talks in Vienna, said the participants were "united in resolve to preserve" the nuclear agreement.

Schmid said that the US cannot launch the process to reimpose UN sanctions on Iran using a Security Council resolution enshrining a deal they have abandoned.

In a boost to Tuesday's talks, Iran last week agreed to let UN nuclear inspectors visit two sites suspected of having hosted undeclared activity in the early 2000s.

Rouhani said he had spoken to the current Security Council president, Abdou Abarry of Niger, who he said "shared our views" that the US cannot reimpose international sanctions.

The Security Council last week blocked the US bid to reimpose sanctions.

Washington also failed to rally enough support to extend an arms embargo on Iran, that is scheduled to begin being rolled back from October.

Rouhani hailed the pushbacks against the US as a "victory" for Tehran and a "disgraceful failure" for Washington.