The United States and its allies expressed cautious optimism as they awaited Tehran's final response to the make-or-break offer of a deal to persuade Iran to end its uranium enrichment programme. Proposals were delivered at a two-hour meeting in the Iranian capital by Javier Solana, the European Union's foreign policy chief, on behalf of France, Britain, Germany China, Russia, and the US - and drew a surprisingly measured initial response from the regime.
The package had "some positive steps" but also some "ambiguities," Ali Larijani, the chief Iranian nuclear negotiator said.
In Washington, Tony Snow, President Bush's spokesman, said the White House had been heartened that the offer was apparently being taken seriously.
It is a promising sign that details of the offer from the "EU three" and the other permanent members of the United Nations Security Council have not been made public by either side.
Neither Mr Snow nor any other US official would confirm the outlines of the package - said to include spare parts for Iran's elderly civilian airliner fleet, a lifting of US sanctions on the export of American agricultural, and support for Iran's civil nuclear programme, with the supply of light-water reactors. The major powers would also back Tehran's membership of the World Trade Organisation, according to The New York Times.
If Iran does not accept the proposals, carrots are likely to be replaced by sticks such as an arms embargo, the freezing of external bank accounts and visa restrictions on the travel of Iranian officials.
Anything more drastic - let alone the threat of military action - would probably be opposed by Russia and China, which both have major economic and energy interests in Iran.
The key, however, remains Tehran's willingness or otherwise to comply with Washington's condition for its direct involvement in the talks: the suspension of Iran's uranium enrichment activities, which the US and its allies suspect is aimed at securing a nuclear weapon.
Iranian officials were studiously vague on that point yesterday. As Mr Larijani spoke of "ambiguities," the Iranian Foreign Minister, Manouchehr Mottaki, noted that any deal should be based on "observing the rights of the Iranian nation". In the past, the regime has insisted on its right to master all parts of the nuclear cycle, including the enrichment of uranium.
It is also unclear how long Iran has been given to make up its mind. When she announced the US about-turn last week in agreeing to direct talks with Iran, Condoleezza Rice, the Secretary of State, said an answer should come "within weeks not months".
Her words reflected the widespread fear, not just here but in Europe, that Tehran will try to spin out the negotiating process, to win time to press ahead with its uranium-enrichment programme.
Nonetheless, even a conditional offer of direct negotiations and the partial lifting of sanctions are the biggest steps taken by the US towards an accommodation with Iran since diplomatic relations were severed in 1979 during the US embassy hostage crisis, after the overthrow of the Shah, Reza Pahlavi.
Iran's suspicion of the US dates back to the CIA-backed coup in 1953 which overthrew the government of Mohammed Mossadegh, who had ties with Moscow, and reinstalled the young Shah in power.
For 25 years, Washington has operated a virtually total ban on links with Iran, accusing the regime of not only seeking nuclear weapons, but of fomenting terror and deliberately undermining the Israeli-Palestinian peace process.
In March 2000, the Clinton administration made a small gesture by lifting sanctions on imports of rugs, caviar and pistachio nuts, after gains by moderates in that year's Iranian parliamentary elections.
But even before the 11 September 2001 attacks on the US, and the branding in 2002 of Iran as a member of the "axis of evil" along with Iraq and North Korea, President Bush had ruled out further steps towards rapprochement.