WASHINGTON - The US and its allies have expressed cautious optimism as they begin the wait for Tehran's considered response to the make or break offer of a package to persuade Iran to end its uranium enrichment programme.
The 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.
The deal had "some positive steps" but also some "ambiguities", said Iranian chief negotiator Ali Larijani.
White House spokesman Tony Snow said the President had been heartened by the fact that the offer was apparently being taken seriously.
One sign that the discussions are for real is that - thus far at least - details of the offer from the "EU three" and the other permanent members of the UN Security Council have not been made public by either side.
Neither Snow nor any other US official would yesterday even confirm the outlines of the package - said to include spare parts for Iran's civilian airliners, a lifting of US sanctions on US agricultural goods, and support for Iran's civil nuclear programme, with the supply of light-water reactors.
If Iran does not go along however, carrots would be replaced by sticks, or "disincentives". These are likely to include a broad arms embargo, the freezing of external bank accounts and visa restrictions on the international travel of senior Iranian officials.
Anything more drastic - let alone the threat of military action - would almost certainly 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 uranium enrichment, which the US and its allies suspect is aimed at securing a nuclear weapon.
Yesterday Iranian officials were studiously vague on that point. As Larijani spoke of "ambiguities", Iranian Foreign Minister Manouchehr Mottaki noted any deal should observe "the rights" of Iran. 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. A senior US official said yesterday that no deadline had been set, but when she announced the US about-turn last week in agreeing to direct talks with Iran, Secretary of State Condoleezza Rice said an answer should come "within weeks not months".
Her words reflected the widespread fear that Tehran will try to spin out the negotiating process, to win time to press ahead with its enrichment.
Nonetheless, even a conditional offer of direct negotiations and the partial lifting of sanctions is the biggest step taken by the US towards an accommodation with Iran since diplomatic relations were severed with the 1979 US embassy hostage crisis, after the overthrow of Shah Reza Pahlavi.
In fact, Iran's deep suspicion of the US dates back to the CIA-backed 1953 coup which overthrew the Government of Mohammed Mossadegh, the Prime Minister suspected of close sympathies with Moscow, and re-installed the young Shah in power.
For the past 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 terrorism 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 September 11 attacks, and his branding of Iran as a member of the "axis of evil" with Iraq and North Korea, President George W. Bush had ruled out any further steps towards rapprochement.
The only contacts have been ad hoc talks between officials on Afghanistan in late 2001 and 2002. Last year the Administration put out feelers for similar contacts dealing with Iraq, but these apparently came to nothing.
* On her first trip to Europe as Secretary of State in February last year, Condoleezza Rice was made aware of the depth of concern about the US threat of military action against Iran.
* She persuaded President George W. Bush to back the European drive to coax Iran into suspending its nuclear programme through incentives.
* At a dinner in New York on May 8, Russian Foreign Minister Sergei Lavrov made it clear to Rice that the Russians would not countenance any threat of UN sanctions against Iran.
* Days later, Rice offered Iran the first talks with the United States in 27 years - on condition that Tehran suspends its uranium enrichment programme.