In response, the six gave Iran two weeks to respond to their demand, setting the stage for a new round of U.N. sanctions.
Iran's refusal to consider suspending enrichment was an indirect slap at the United States, which had sent Undersecretary of State William Burns to the talks in hopes the first-time American presence would encourage Tehran into making concessions.
Diplomats at the negotiating table refused to characterize the two-week time frame as an ultimatum - but it was clear the offer was a de-facto deadline for Tehran to show flexibility.
EU envoy Javier Solana said Iran still has to answer a request made on behalf of the five permanent U.N. Security Council members plus Germany to "refrain from any new nuclear activity."
"We have not gotten all the answers to the questions," Solana told reporters after apparently unsuccessful daylong talks, adding that the two weeks should allow Iran to come up with "answers that will allow us to continue."
American officials were blunter.
"We hope the Iranian people understand that their leaders need to make a choice between cooperation, which would bring benefits to all, and confrontation, which can only lead to further isolation," U.S. State Department spokesman Sean McCormack said in Washington.
In diplomatic terms, "further isolation" is shorthand for economic and political sanctions.
Keyvan Imani, a member of the Iranian delegation, cast doubt over the value of talks less than an hour after they started Saturday.
"Suspension - there is no chance for that," he told reporters in the courtyard of Geneva's ornate City Hall, the venue of the negotiations.
Imani also downplayed the presence of Burns - even though the Americans had previously said they would not talk with the Iranians on nuclear issues unless Tehran was ready to stop all enrichment activity.
"He is (just) a member of the delegation," Imani said.
However, Solana said America's participation in Geneva had shown Iran a united international front, reports CBS News correspondent Elizabeth Palmer.
"[Burns] has contributed a lot," Solana told CBS News. "His presence is also a very important contribution."
John Bolton, who has served as Washington's former ambassador to the U.N and as undersecretary of state in charge of the Iran file, said the outcome proved that Tehran never had "serious intentions to give up its nuclear program."
"I think maybe this will convince the Europeans to take stronger steps," he told The Associated Press, alluding to the possibility of harsher EU sanctions than the existing European penalties on Iran.
Chief Iranian negotiator Saeed Jalili evaded the issue of suspension, demanded as part of the six-power "freeze-for-freeze" proposal that carries a commitment of no new U.N. sanctions in exchange for an Iranian pledge to stop expanding its enrichment program.
Instead he spoke in generalities about the need for cooperation and constructive exchanges of ideas that reflected Tehran's reluctance to focus on the six-power offer.
"Iran is calling on the Western powers to resume the dialogue," he said.
Iranians were watching these talks closely too and many will be disappointed by the outcome, reports Palmer.
They blame high inflation and unemployment on tough financial sanctions against Iranian banks and businesses and know a diplomatic solution could bring big benefits.
Iran already is under three sets of U.N. sanctions for its refusal to suspend enrichment, which can generate both nuclear fuel and the fissile material at the core of nuclear warheads. While Tehran says it has a right to enrich for peaceful purposes, the sanctions reflect international concern that it might use its program to make weapons.
The "freeze-for-freeze" offer delivered to Iranian officials last month by Solana envisions a six-week commitment from Iran to stop expanding enrichment in exchange for a six-week moratorium on new sanctions. That aims to lead to formal negotiations in which the six nations hope they can persuade Tehran to indefinitely ban enrichment.
Burns' decision to attend the Geneva talks showed that Washington was willing to temporarily accept the "freeze-for-freeze" plan - something less than fully mothballing the program as it had always demanded.
Recent Iranian statements had suggested Tehran was looking to improve ties with the United States, with officials speaking positively of deliberations by the U.S. administration to open an informal diplomatic presence in Tehran after closing its embassy decades ago.
Iran and the United States broke off diplomatic relations after the 1979 Islamic Revolution and the hostage crisis at the U.S. Embassy in Tehran. U.S. interests in Iran are now represented by the Swiss Embassy in Tehran.
Imani said Tehran had not yet received a proposal from the U.S. on a representation bureau but would "study it positively" if it did.
U.S officials had earlier said Burns was at the table to listen only, describing his presence as a one-time occasion. But McCormack said he did speak.
Burns delivered "a clear simple message" when it was his turn to speak, McCormack told reporters in Washington. He quoted Burns as telling his Tehran counterpart: "Iran must suspend uranium enrichment to have negotiations involving the United States."
The U.S. said the Geneva talks would focus only on the nuclear issue, but Iranian Foreign Minister Manouchehr Mottaki said earlier this week the two nations also were considering the issue of direct flights between the two countries.