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Iran has gradually scaled back its commitments under the nuclear accord - signed with the United States, China, Russia, Germany, France and the United Kingdom - in retaliation for Washington's withdrawal from the pact in 2018 and its reimposition of devastating sanctions.
Earlier in the week, the UK, France and Germany challenged Tehran over breaking the limits set out in the agreement by triggering a "dispute mechanism". Some analysts suggested that could spell the end of the accord.
"We are enriching more uranium before the deal was reached ... Pressure has increased on Iran but we continue to progress," Rouhani said in a televised speech.
He added the nuclear programme is in a "better situation" than it was before the nuclear deal was signed.
Iran has only modestly increased its nuclear activity after the US pullout. In recent months it boosted its enrichment of uranium to 4.5 percent - higher than the 3.67 percent limit set by the agreement, but far from the 20 percent enrichment it was engaged in before the deal.
Uranium must be enriched to 90 percent to be used in a nuclear weapon.
Rouhani defended the 2015 nuclear deal in his speech saying: "We have proven in practice that it is possible for us to interact with the world."
'A lot of concern'
Aniseh Bassiri Tabrizi, from the Royal United Services Institute, said the comments over the past few days indicate that posturing by the European nations and Iran is fully under way.
She added it has yet to be confirmed how much enrichment the Iranians actually carried out.
"There is going to be a lot of concern after the announcement by the Iranian president, but we have to keep in mind the IAEA [International Atomic Energy Agency] has control over oversight on nuclear activities, so there isn't anything going on that the international community wouldn't be aware of ... We should really wait for the IAEA's assessment," Tabrizi told Al Jazeera.
The European nations announced they triggered the dispute mechanism provided for in the historic agreement in order to force Tehran to honour its commitments under the accord, formally known as the Joint Comprehensive Plan of Action (JCPOA).
On Thursday, the European Union's top diplomat Josep Borrell held direct talks with Iran's Foreign Affairs Minister Mohammad Javad Zarif in New Delhi.
Borrell said the bloc is still committed to saving the deal.
"In a frank dialogue, they discussed the latest developments around the Joint Comprehensive Plan of Action," the EU said in a statement.
The face-to-face talks on the sidelines of a conference were the first following a series of telephone calls since a US drone strike killed top Iranian general Qassem Soleimani on January 3.
Borrell said the nuclear deal is "now more important than ever in light of the dangerous escalations in the Middle East and the Gulf region".
'Prevent military confrontation'
Tensions in the region have simmered in recent months after a series of attacks in the Gulf region that the US blamed on Iran and aligned groups, despite denials from Tehran.
Fears of a military escalation soared in early January after the assassination of Soleimani in Baghdad, prompting Iran to fire a barrage of missiles at a military base housing US troops in Iraq.
In his speech on Thursday, Rouhani said the Iranian retaliation - which caused significant material damage but no casualties according to the US military - strengthened Iranian deterrence against the "threats" by US President Donald Trump.
But despite the continuing tensions, Rouhani said Tehran was working daily "to prevent military confrontation and war" and dialogue with the world remained "possible".
The 2015 nuclear deal imposed restrictions on the Iranian nuclear programme in exchange for a reprieve from international sanctions.
After unilaterally withdrawing, the US has reimposed a range of sanctions on Tehran and called for negotiations over a new accord.
Iran has rejected the idea of negotiating a new deal while it is under sanctions.
In response to the US move, Tehran has begun enriching uranium above the cap agreed in the deal and taken further steps to enhance its nuclear programme, while also accusing the European parties to the deal of failing to live up to their own commitments to provide economic relief to Tehran.
Al Jazeera's Assed Baig reporting from Tehran said Rouhani had sent a defiant message to the world, saying Iran is reducing commitments, but also adding the reductions are reversible if European countries return to their obligations to that deal.
"He's saying to European countries that they need to stand up to the US," Baig said.
"These sanctions have hit Iran's oil sector, the banking sector and the economy and he accepted this - that Iran's oil exports have been reduced, but the economy is still working, according to Rouhani."
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