It's also reversed the Trump administration's determination that all U.N. sanctions against Iran had been restored and eased stringent restrictions on the domestic U.S.travel of Iranian diplomats posted to the United Nations.
Earlier on Thursday, the E3, the three European participants in the deal, and the United States released a joint statement warning Iran against going through with that step.
Under the 2015 deal, Iran agreed to allow teams from the International Atomic Energy Agency into its nuclear facilities.
The Trump administration withdrew from the Iran deal in 2018 and imposed heavy sanctions on Tehran that left the country's economy in shambles.
However, the Iranian presidency said Rouhani in the call "criticised Europe's performance" on its JCPOA commitments after the USA withdrawal.
German Chancellor Angela Merkel on Wednesday held a telephone call with Iranian President Hassan Rouhani in which she voiced her "concern" over Tehran's non-compliance with the 2015 Joint Comprehensive Plan of Action (JCPOA) nuclear pact, her spokesman said.
The diplomats noted "the unsafe nature of a decision to limit IAEA access, and urge Iran to consider the consequences of such grave action, particularly at this time of renewed diplomatic opportunity".
"Iran should reverse these steps and refrain from taking others that would impact the IAEA assurances, on which... the entire world relies", US Department of State spokesperson Ned Price said.
Analysts say only a small window of opportunity remains to save the deal as Tehran ramps up its nuclear work in retaliation against the reimposition of sanctions that followed the USA walkout.
Democrats applauded the development, noting their view that the Trump administration's maximum-pressure campaign had brought Iran close to obtaining a nuclear weapon.
On Thursday, Secretary of State Antony Blinken said that the Biden administration would reenter talks about the JCPOA with Iran and the other nations that negotiated the original agreement. Last month, Tehran announced that it had begun enriching uranium to a purity level of 20%, which is five times the limit set by the JCPoA.
German Foreign Minister Heiko Maas said earlier that Iran's recent steps were endangering the prospect of the United States returning to the deal, warning that Iran was "playing with fire". "Remove the cause if you fear the effect", he continued. "We did not think that in America a insane person would be elected and start a historically incomparable war against the nation", said Rouhani, referring to the crippling economic sanctions as an "economic war".
In Iran, President Hassan Rouhani expressed hope Thursday that the Biden administration will rejoin the accord and lift the USA sanctions that Washington re-imposed under Trump, according to state television. Besides overcoming disagreements over the sequencing of an agreement, the United States also intends to lengthen and strengthen the deal to restrain Iran's ballistic missile program and curb its support for proxy militias across the Middle East. Iran opposed such terms during its negotiations with the Obama administration.
This would involve Washington revoking Trump's 2018 withdrawal and green-lighting an Iranian request for an emergency International Monetary Fund loan, while Iran freezes "the most problematic aspects" of its nuclear programme, he said.