Although a first round of talks with the five permanent members of the Security Council on Wednesday made little progress, Mr Annan plans to repeat the exercise today, and British officials professed themselves "not discouraged" with the outcome.
If the five can agree on a clear enough mandate, the Secretary General could yet travel to Baghdad - as the Iraqis themselves have long been urging. But Mr Annan says he will not go until a deal is at hand. The two sides had taken "a few steps forward," but there was still a "long way to go".
Reaching agreement within the Security Council will be almost as tough as finding one with Baghdad.
While Britain and US are uncompromising that Saddam must fully comply with existing UN resolutions or face the prospect of military strikes, France and China are opposed to the use of force, while Russia's ferocious hostility visibly shocked William Cohen, the US Defense Secretary, when he visited Moscow yesterday.
Complicating matters is the possibility of a further UN resolution on Iraq. Britain maintains that existing UN resolutions authorise the use of force, but would none the less like to see another one now - as a "strong signal," a senior Foreign Office official put it, which would be a "final warning" to Saddam.
But its tabling is being held up by the differences on the Security Council, and any text that could be agreed might be so weak that it only advertises the disunity of the international community over an attack.
Failure to agree anything would simply underline those divisions even more sharply - which is why the US is profoundly suspicious of the whole enterprise.
In the meantime, despite offers of logistical assistance dribbling in from various European capitals, the EU's heart is plainly not in the enterprise.
In the Gulf, Foreign Office minister Derek Fatchett wound up a visit to Oman and the United Arab Emirates, claiming opinion in the Gulf was hardening against Saddam, but most other Arab countries, as well as Iran, oppose the use of force.
British officials believe the next few days will show whether a deal is possible. "The door remains open," they say - by coincidence or otherwise, exactly the phrase employed by the Iraqi Foreign Minister Mohammed Saeed al-Sahaf yesterday after a meeting with the Arab League in Cairo.
But the US military build-up continues relentlessly, with the announcement that a further 40 aircraft including F-117 Stealth fighters and B-52 heavy bombers will be going to the Gulf. Two Patriot anti-missile missile batteries - flawed stars of the 1991 war - have already been dispatched to the region.
Notwithstanding the unyieldingly tough talk by the US, a sense is growing that diplomacy may yet stave off the worst. Taken at face value, a declared British readiness to look at "special arrangements" for the inspection of Saddam's presidential palaces does not amount to much.
Whatever these arrangements, they will have to include the right for repeat inspections, and contain no time limit on them. Richard Butler, the head of UNSCOM must also take part. And, Britain and the US insist, the Iraqi undertakings must be in writing.
But, some diplomats say, brinkmanship is starting to budge the fast-frozen diplomatic ice floes.
The UN is in the thick of things, and Baghdad's revised offer of a two month inspection period for eight "presidential palaces", though already rejected by Washington, London and Paris, may not be its last.Reuse content