Cyrus Razzghi, a western-educated businessman and president of ARA Enterprise, said: "The taboo of talking to the Americans is now completely broken . . . it will become more difficult for either party to demonize each other in the coming days and months."
A smiling Mr Rouhani said in a brief press conference: "There is a long way before us but the first step has been taken."
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Advisers to the new government, who declined to be named, warned that the president faces daunting challenges in turning round an economy starved of credit thanks to the international sanctions. "The challenge for Rouhani at home is 10 times more difficult that what he faces abroad."
Among self-styled hardliners who have long lobbied against any concessions to the US, the response was one of restrained criticism, aware that Ayatollah Ali Khamenei had tendered his support for the deal.
Hossein Shariatmadari, editor of Kayhan, the conservative newspaper, said the deal was "not a big event".
He used a popular metaphor to describe how Iran has lost the initiative in the negotiations: "A thief steals your jacket. You shout you want it back, but the thief then takes your hat. You fight and fight over the jacket, and then you get your hat back. By now you have forgotten about your jacket and what the original fight was about. That is our story."
(Read more: Iran curtails nuclear capacity expansion: IAEA)
While the interim deal has opened the prospect of a thaw in Iran's relations with the US, hopes of consolidating the Geneva agreement remain guarded on all sides.
Apart from opposition from third parties, notably Israel and Saudi Arabia, there are doubts about Iran's willingness to go significantly further in curbing its nuclear ambitions as part of a comprehensive settlement.
The agreement with Iran was criticized by senior members of the US Congress on Sunday.
Ed Royce, the Republican chair of the House foreign affairs committee, said that while Iran was keeping the "key elements" of its nuclear program, "we are the ones doing the dismantling" by providing sanctions relief that was a "lifeline" to the Iranian regime.
(Read more: Kerry: Iran nuclear talks face 'important gaps')
Marco Rubio, a Republican senator from Florida, said the agreement shows "other rogue states that you can obfuscate, cheat and lie for a decade and eventually the United States will tire and drop key demands".
Although there is strong support in Congress for new sanctions, leading senators were careful on Sunday to describe legislation that would not immediately clash with the administration's negotiating position over the next six months.
Robert Menendez, the Democratic chair of the Senate foreign relations committee, said sanctions legislation should "provide for a six-month window to reach a final agreement before imposing new sanctions on Iran, but will at the same time be immediately available should the talks falter or Iran fail to implement or breach the interim agreement".