He also pledged that Iran would not give up its nuclear programme and insisted that seeking an accord with the West had not damaged its progress.
"This path of negotiation will reach a final agreement," Rouhani said on state television.
"Most of the gaps have been removed," he added, referring to major differences that have so far prevented an interim deal being turned into a comprehensive settlement.
A final agreement is aimed at ensuring Iran will never develop nuclear weapons under the guise of its civilian activities. The Islamic republic denies such intent.
Rouhani urged Iranians to keep faith in the talks despite the failure so far to strike a deal and solve key issues including lifting sanctions and ensuring Iran's future ability to enrich uranium for peaceful purposes.
But he appeared to adopt a softer line on sanctions.
"There is no doubt that sanctions will be lifted. The question is timing," he said.
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"We consider the sanctions to be tyrannical and have to lift them step by step," remarks a step back from demands made by top parliamentary officials that they all be removed at once.
"We will never give up our rights," Rouhani said, referring to the enrichment process.
"During all this time centrifuges were spinning. I promise the Iranian nation that those centrifuges will never stop working."
Rouhani's comments came after US Secretary of State John Kerry told reporters "real and substantial progress" had been made during almost a week of negotiations in Vienna.
Iran and the five permanent members of the UN Security Council plus Germany will now seek to strike an outline deal by March 1 and to nail down a full technical accord by July 1, officials said.
Despite missing Monday's deadline, the parties are working on the basis of an agreement struck a year ago that curbs some of Iran's nuclear activities in exchange for limited sanctions relief.
The talks will resume next month. In view of the difficulties, many experts long believed the negotiators would put more time on the clock.
Iran will keep receiving around $700 million (560 million euros) in frozen funds per month, or $4.9 billion by July, adding to some $7 billion received since January when the interim deal was implemented.
A final agreement could see sanctions that ravaged Iran's economy removed, silence talk of war and deliver a groundbreaking political achievement for Rouhani and a foreign policy success for his US counterpart Barack Obama.