The dispute is over disarmament. Boutros Boutros-Ghali, the UN Secretary-General, maintains that the Bush administration promised that its forces would disarm the factions, while US spokesmen insist they are only here to protect relief supplies and will not attempt to disarm Somalis who do not threaten them.
Mr Boutros-Ghali told the New York Times yesterday that he intended to release a letter he wrote to President Bush after the Security Council resolution of 3 December, in which he set out what he thought the role of the US would be in Somalia. Mr Boutros-Ghali said he understood that the US had discreetly promised to pacify the country by disarming the factions. But yesterday at the UN he played down what he called differences with Washington over the disarming of the country.
Yesterday Lawrence Eagleburger, the US Secretary of State, confirmed the existence of the letter. A US spokeswoman in Mogadishu, Rene Bafilis, said it was her understanding the letter did not contain the words 'disarmament' or 'disarm'. A UN spokesman, Ian Macleod, said the letter did contain those words. The marines' spokesman, Colonel Fred Peck, told journalists that: 'We are not here to disarm the Somali people.'
In Baidoa tomorrow the US forces will meet the victims of starvation they have come to save. More than 50 people are dying daily in the small town 200 miles west of the capital, where banditry and faction fighting have prevented the distribution of food aid. Two US officials are already in the town and Robert Oakley, the US special envoy, is expected there today. The gunmen, who have dominated the town for several weeks, are said to be moving out and are not expected to resist the US forces.
The takeover of Baidoa will give the operation renewed hope. During the past week there has been mounting frustration at the build-up of US forces in Mogadishu in front of the television cameras while people continued to starve to death three hours' drive away.
In Mogadishu there are now 4,000 US marines and they are being joined by forces from France, Belgian, Botswana, Italy and Saudi Arabia.
US officials here continually stress the depth of US commitment to Somalia. 'We will stay as long as it takes,' one said. 'We are not going to be like the good guy who comes into town and shoots up all the bad guys and as he rides into the sunset, someone says 'and he never even told us his name'.' At the same time, they stress that their role is humanitarian. They are here to provide security for emergency food distribution. They say it is the United Nations' role to help put the country back together again - and to organise disarmament.
The impact of the US operation in this poor, broken country has been visually stunning but the US watchword so far has been caution. 'We want to minimise absolutely the risk to our own forces,' said the operation commander, General Robert Johnston, on Sunday.
The military planners work on the assumption that every armed Somali is hostile and will fight. Hence the full-scale assault on the port and the airport last week, despite the fact that the Pakistanis' UN peace-keeping force had held the airport since 10 October. It then took the marines three days to consolidate before they moved inland. They have now taken over the US embassy in Mogadishu and are running patrols, escorting food convoys and flying Cobra helicopters low over the city.
On Sunday they took over the airport at Balidoogli, 60 miles inland. Soon they will move further and reach some of the areas where food for the starving people is being blocked by gunmen.
On Saturday the US spokesman said a Cobra was fired on and, returning fire, it destroyed three vehicles - dramatically illustrating the rules of engagement. If US forces are approached by anyone carrying a gun in a threatening way, they will 'deal with' the perceived threat appropriately. But that is the limit. 'There will be no house-to-house searches or searching of cars,' said Colonel Peck.
The effect of this cautious policy has been to drive the heavy weapons off the streets of Mogadishu. Some 'technicals' have been gathered together in special areas but these are only some of the ones 'controlled' by the political leaders. Others have gone into the interior and have caused new clashes with local clan militias, and their crews have resorted to pillage and killing. Most have been hidden. In Mogadishu, robberies have soared, Western journalists being one of the main victims. Guns are now carried more discreetly but are no less effective. It is impossible for a Cobra helicopter to prevent street crime.
On the political front the Americans scored a success by bringing together Ali Mahdi Mohamed and General Mohamed Farah Aideed, the two barons of divided Mogadishu, enabling them to formalise their nine-month-old ceasefire. It is too early to assess the popularity of the Americans but many who welcomed them are now worried about their over-cautious but heavy-handed tactics, while the fighters are fearful and resentful.
If things go well, it is possible that in a month's time the international forces, at full strength, will have established their presence throughout the famine area and food will be reaching everyone in need under armed escort. It is also possible that, at the same time, the warlords and fighters will be enjoying a rest and, with their arsenals full but hidden, they will be waiting to resume their wars as soon as the Americans leave.
The US and UN differences over disarmament will not be easily resolved. It is possible that the American military do intend to take on the factions' armies and disarm them but have judged it tactically foolish to announce this until they are powerful enough to do it. But Mr Oakley said on Sunday: 'It is a clearly defined mission, which is to establish security conditions in Somalia to provide for the uninterrupted flow of relief supplies. It does not include disarmament.'
He was supported by Gen Johnston, who said: 'There are so many weapons it would be a task which is enormous.' It is hard to imagine international troops searching under the beds for guns like Mohamed's in the back streets of Mogadishu. And where would it stop? Would they move into northern and north-eastern Somalia to disarm the factions there as well?
If the US forces think the task too great to achieve militarily, it is certainly impossible for the UN. There is more hope politically, but the UN is neither a credible military nor political force in Somalia.