Germany was also positive, saying the latest talks had boosted hope for a diplomatic solution but a wary Russia warned there was "no reason to break into applause."
"It was decided to convene the next meeting in Geneva on ," European Union foreign policy chief Catherine Ashton told reporters.
She read from what she underlined was an unprecedented joint statement agreed with Iranian Foreign Minister Mohammad Javad Zarif and herself as chair of the international negotiating team.
The EU is at the helm of the so-called P5+1 group — Britain, China, France, Russia and the United States, plus Germany — which has spent years trying to reach a deal with Iran amid fears that it is developing nuclear weapons.
The Islamic republic vehemently denies that and insists its nuclear programme is for peaceful purposes.
The talks were the first between all parties' nuclear negotiators since
They ended a six-month freeze over Iran's refusal to curb uranium enrichment in exchange for easing the international sanctions battering its economy.
"We hope that this a beginning of a new phase in our relations," Zarif told reporters.
While the details remain under wraps, Iran's lead nuclear negotiator Abbas Araqchi said its proposal involved "proportionate and reciprocal steps by both sides".
Iran's plan contains three steps that could settle the nuclear dispute "within a year", Araqchi has said, the first achievable "within a month or two, or even less".
He said that snap inspections of Iran's atomic facilities were part of the last step.
White House spokesman Jay Carney said Iran's presentation at the talks was "useful", showing a "level of seriousness and substance that we have not seen before."
In Geneva, a senior US official said: "I have never had such a detailed, straightforward, candid conversation with the Iranian delegation."
But there was a note of caution.
"The devil is truly in the detail in this particular subject . . . although we got more today than we've ever gotten, there is a whole more that we need to get, the official said.
"Probably a whole lot more Iran wants to get from us."
German Foreign Minister Guido Westerwelle said the talks had "reinforced hope that a diplomatic solution is possible to completely calm our concerns about the nature of the Iranian nuclear programme."
But Russian negotiator Sergei Ryabkov was less than upbeat.
Ryabkov agreed that the results were better than April's round in Kazakhstan — when Ahmadinejad was in power, and the talks hit the wall.
"But this does not guarantee further progress," he said.
Iran has already drawn red lines, saying it will not accept demands to suspend uranium enrichment or ship stockpiles of purified material abroad.
"We will not back down on our rights," Zarif said.
"At the same time we feel there is no need for concerns about our nuclear program… it is logical to remove any concerns though," he added.
"We entered into details about the first and final steps . . . differences still exist and there are a number of them," Araqchi said.
While Western negotiators insist they will never leave room for Iran to develop atomic weapons, Israel, the Middle East's sole if undeclared nuclear-armed power, has sounded the alarm over the thaw.
Israel's International Relations Minister Yuval Steinitz said the country was watching the talks "with hope and with concern".
"We see the worrying signs and we don't want Geneva 2013 to turn into Munich 1938," he said on Israel's army radio, referring to Britain and France's failed bid to avert war by agreeing to Nazi Germany's annexation of swathes of Czechoslovakia.
Israel has not ruled out a military strike to halt Iran's nuclear drive.