Although Mr Schröder deliberately avoided the Democratic candidate, John Kerry, during his two-day trip to the US, there is little doubt that a Kerry victory would provoke rejoicing inside Germany's government, as it would in many other parts of Europe, as well as Asia, Africa and Latin America.

This week Mr Kerry claimed that foreign leaders had told him they could not publicly offer him their support but added: "You've got to beat this guy, we need a new policy."

Hostility towards a second Bush term is generally assumed to be widespread throughout the world because of the Iraq war, the concept of pre-emptive strikes and bullying of small countries. On issues from the Kyoto agreement and the international criminal court to antipathy towards the UN, President Bush has alienated countries Washington would normally classify as allies.

Distress over Mr Bush's foreign policy is not confined to the world beyond the US. According to a Washington Post-ABC News poll yesterday, 57% of Americans want their next president to steer the country away from the course set by the current leader.

Asked how much support Mr Bush had worldwide, Dana Allin, senior fellow for transatlantic affairs at the London-based International Institute for Strategic Studies, said: "Not a lot. There is a conventional wisdom about US elections for foreign policy: that the incumbent is always preferred because of [established] relations and predictability. This is an election where that pattern is broken. There is a perception, for better or worse, that there has been a departure from the tradition of American foreign policy."

It is difficult to assess the level of opposition to Mr Bush. When he put together a "coalition" for the war against Iraq last year he gathered just 43 countries - and it was an odd collection that included countries such as Azerbaijan, Eritrea and Uzbekistan, not normally in the forefront of international diplomacy.

Tom Ridge, the US homeland security secretary, told diplomats and academics gathered in Singapore yesterday that 70 countries had joined an informal alliance against terrorism. But this is no evidence of support for Mr Bush; there are leaders who will think it prudent to back the world's sole superpower though privately they would welcome a Kerry presidency.

Mr Schröder's spokesman last night denied he was one of the "foreign leaders" who had sent a secret message of support to Mr Kerry.

Victor Bulmer-Thomas, director of Royal Institute for International Affairs, in London, said yesterday he doubted if any head of government had been unwise enough to say in private to Mr Kerry that they wanted him to win and thought it more likely that the "foreign leaders" to whom the Democratic candidate referred to were foreign secretaries or heads of parliamentary delegations.

He said there was a difference between how a second Bush presidency was perceived by the "masses" - who wanted shot of Mr Bush in the belief there would be a return to a golden age - and the elite - who were not convinced there ever had been a golden age and leaned towards "better the devil you know".

Unsurprisingly, this does not seem to be the view in France. "It's clear that Bush is widely disliked in France, even by the right," said Guillaume Parmentier of the France-America Centre. "The whole country and the government would rejoice if he lost. But although the tone of a Kerry administration would certainly be different, many difficulties would remain."

A French foreign ministry official, who asked not to be identified, concurred: "Things might feel better, but they might not be better."

Spain's prime minister, José María Aznar, and Italy's prime minister, Silvio Berlusconi, are unequivocal in their support of Mr Bush, as are many eastern European countries and former Soviet republics. But opinion in Spain, as in Britain, is divided. The Spanish opposition leader in the general election this Sunday, the socialist José Luis Rodríguez Zapatero, said yesterday: "I think Kerry will win. I want Kerry to win."

The position of Tony Blair and of the Russian president, Vladimir Putin, is ambiguous.

In the Middle East there is overwhelming antipathy for a second Bush term. The Egyptian political columnist Salama Ahmad Salama said in Cairo yesterday: "The mood in Egypt is that nobody wants Bush any more. He has built a big reservoir of suspicion and doubt, and a bit of hate. I don't think anybody in the Middle East will welcome his staying."

Israel has benefited from the Bush presidency but it would probably have few problems in embracing Mr Kerry, whose emotional article expressing support for the country has been widely circulated.

Members of the Iraqi governing council have mixed feelings, even though the US president's war opened the way for them. One said he was unimpressed with the handling of postwar Iraq but would not welcome an abrupt change of personnel, let alone of policy. A source in the Iraqi foreign ministry said: "We are relaxed about the idea of a Kerry presidency, provided he doesn't sell us down the river in order to gain votes."

Most Pakistanis claim to despise Mr Bush for what they consider America's unjustified attack on Iraq. But regime change in the White House is probably the last thing President Pervez Musharraf would really want. "The government would like Bush to win," said Tahir Mirza, editor of the Dawn, a leading daily paper. "We've always been pro-Republican - we think the Republicans are much more sympathetic to Pakistan. And, in the present case, they've given us a lot of money."

Additional reporting: Brian Whitaker, Jon Henley in Paris, Giles Tremlett in Madrid, Michael Howard in Baghdad and James Astill in Islamabad

How the world lines up

How foreign leaders are believed to view the rivals:

For Kerry
Germany
France
Entire Arab world
Most of Latin America

Neutral/unknown
Britain
Russia
Israel
Iraq