Philippe Douste-Blazy, the French foreign minister, who along with his British and German counterparts has spearheaded diplomatic moves with Tehran, said the US policy shift "reinforces the credibility" of Europe's efforts.
Margaret Beckett, the British foreign secretary, said: "I urge Iran to respond positively to this opportunity."
In Berlin, Frank-Walter Steinmeier, the German foreign minister, told a press conference that Washington's offer was "a real strengthening of American efforts".
"I see a window opening" which could bring about a solution, Steinmeier said, flanked by his Dutch counterpart Ben Bot.
Both ministers said they hoped Iran would understand the significance of the offer and seize the opportunity.
Israel, thought to have the only atomic arsenal in the Middle East, has long called for action from its US ally against Iran, accusing it of seeking nuclear weapons.
Tzipi Livni, the Israeli foreign minister, said in a statement: "Israel appreciates the steps and measures by the United States in continuing to lead the international coalition and in taking all necessary steps to prevent Iran from gaining nuclear capability."
Meanwhile, Mohamed ElBaradei, director-general of the International Atomic Energy Agency (IAEA), said he "strongly encourages Iran to create the conditions necessary for the resumption of these talks [with the European Union], with US participation, with a view to achieving a comprehensive settlement that is acceptable to both the international community and Iran".
Javier Solana, the EU foreign policy chief, said US participation "would be the strongest and most positive signal of our common wish to reach an agreement with Iran".
"This important statement by the US administration reinforces our hope that out of the current discussions we will be able to establish a new and cooperative relationship with Iran, based on mutual confidence," he said.
Sergey Lavrov, the Russian foreign minister, visiting Turkey, said: "We hope the way will be open to a political solution after the talks in Vienna."
In a policy shift, US Secretary of State Condoleezza Rice said Washington was ready to join direct talks with Europe on Iran's nuclear programme if Tehran suspends all uranium enrichment activities.
Washington heavily backed the former Iranian imperial government of the Shah, which was toppled in 1979 and replaced by an Islamic republic headed by Ayatollah Ruhollah Khomeini.
The Iran government had no immediate comment on the US proposal, but the foreign policy spokesman for its parliament reportedly said the precondition was "not suitable".
Kazem Jalali, spokesman for parliament's foreign policy and national security committee, said in comments carried by Iran's student news agency ISNA: "The fact that the US has announced its readiness for talks can be viewed as positive, but the US precondition is not suitable.
"The Islamic Republic of Iran has announced that it does not have halting enrichment on its agenda."