In a speech broadcast on national television on Wednesday, Rouhani said the remaining signatories - the United Kingdom, France, Germany, China and Russia - had 60 days to implement their promises to protect Iran's oil and banking sectors from US sanctions.
Rouhani said Iran wanted to negotiate new terms with remaining partners in the deal, but acknowledged the situation was dire.
"We felt that the nuclear deal needs a surgery and the painkiller pills of the last year have been ineffective," Rouhani said. "This surgery is for saving the deal, not destroying it."
Since then, the US has restored crippling economic sanctions on Iran, even as Tehran continued to abide by the deal, according to United Nations inspectors.
Rouhani announced Iran would roll back some of its commitments under the 2015 nuclear agreement, saying it would keep excess enriched uranium, instead of selling it as called for under the deal.
"If the five countries join negotiations and help Iran to reach its benefits in the field of oil and banking, Iran will return to its commitments according to the nuclear deal," Rouhani said.
However, Rouhani warned of a "strong reaction" if European leaders instead sought to impose more sanctions on Iran via the UN Security Council. He did not elaborate.
US Secretary of State Mike Pompeo said his country would wait and see Tehran's next move.
"I think it was intentionally ambiguous," Pompeo said of Iran's announcement. "We'll have to wait and see what Iran's actions actually are" before deciding on a US response.
"They've made a number of statements about actions they threatened to do in order to get the world to jump," said Pompeo.
The United States also accused Iran of engaging in "nuclear blackmail" after Tehran announced it would no longer abide by the limits of its 2015 nuclear deal.
"America is never going to be held hostage to the Iranian regime's nuclear blackmail," US envoy for Iran Brian Hook said.
'Enough is enough'
Speaking to Al Jazeera from Tehran, Mohammad Marandi, an academic at the University of Tehran, said Iran's patience has run out over the nuclear deal.
"I don't think the Iranians consider the nuclear deal to be dead - although for practical purposes, it has been dead for quite a while," Marandi said.
"Under Obama, the US refrained from implementing the deal, but under Trump, the Americans have become very extremist, and ultimately they have ripped up the agreement. The Europeans, despite promises and nice words, they have been effectively abiding by the dictates of Trump.
"So, the Iranians are saying 'we cannot continue like this, we've been waiting for a year since the Americans exited the agreement, and we have been waiting to see what the Europeans will do. Now that we see they're doing nothing, we have to take some steps'."
Marandi noted Iran made major concessions in signing up for the nuclear deal.
"Now the government has decided enough is enough."
Robert Kelley, a former UN nuclear inspector now with the Stockholm International Peace Research Institute, said the commitments Iran was dropping had no bearing on its ability to develop an atomic bomb.
He said Iran was simply seeking to "save face" after "striking a deal which was not respected by the other side".
Iranian Foreign Minister Mohammad Javad Zarif told his Russian counterpart on Wednesday that Tehran's decision to reduce its commitments was legal, the RIA news agency reported.
Zarif, in Moscow for talks, told Russian Foreign Minister Sergey Lavrov that Iran's actions did not violate the original terms of the nuclear agreement and that Tehran now had 60 days to take the necessary diplomatic steps.
In response to the Iranian move, Israeli Prime Minister Benjamin Netanyahu vowed not to allow Iran to acquire nuclear arms.
"This morning, on my way here, I heard that Iran intends to continue its nuclear programme," Netanyahu said at a ceremony on Israel's annual day of remembrance for its war dead.
"We shall not allow Iran to obtain a nuclear weapon," he added.
Britain said Iran's announcement was disconcerting.
"We are extremely concerned about this announcement and urge Iran to continue to meet its commitments under the deal and not to take escalatory steps," Prime Minister Theresa May's spokesman told reporters.
"This deal is a crucial agreement which makes the world safer and we will ensure it remains in place for as long as Iran upholds these commitments."
Germany urged the Iranian government not to take any aggressive steps. A government spokesman added Berlin wants to keep the Iran nuclear deal, and said Berlin would fully stick to its commitments as long as Iran does the same.
Spokesman Steffen Seibert said work on setting up a special purpose vehicle for business with Iran is taking longer than expected.
"Currently, the last steps need to be taken for this corporation to be able to operate - that includes Iran making the necessary preparations on its side," Seibert told a regular government news conference.
The United States warned European banks, investors and businesses against engaging with the so-called special purpose vehicle (SPV), a Europe-backed system to facilitate non-dollar trade with Iran and circumvent US sanctions.
"If you are a bank, an investor, an insurer or other business in Europe you should know that getting involved in the … special purpose vehicle is a very poor business decision," Tim Morrison, special assistant to the president, told a conference.