The American people may have been deeply divided over their choice of leader, but the rest of the world is remarkably unanimous in its message to the new US president: "Don't ignore us."
"But don't boss us around, either," say political analysts and ordinary citizens from China to Brazil, asked for their advice to the newly reelected President Bush as he looks forward to a second term of office likely to be dominated by the global "war on terror."
Few other countries would have chosen George W. Bush over John Kerry, international polls have revealed. But nobody anywhere doubts the impact that the US president has on his or her life.
If there is one task to which foreigners would like to see Mr. Bush devote himself, to judge by dozens of interviews on four continents, it is to restore America's reputation as a fair and honest arbiter of world affairs, damaged by what many abroad see as the administration's tendency to throw its weight around in its own narrow interests.
"Given that [the president] heads the most powerful nation in the world but that it has the worst reputation of all time, there is a paradox," says Stanley Symington, a retired marketing executive in England. "He should pay more attention to restoring America's reputation in the world, rather than to guarding its security."
It would help, suggests Jagjit Bagga, as he walks around a fashionable shopping center in New Delhi, if the president adopted a more diplomatic tone with the rest of the world. "America shouldn't be arrogant when it deals with other countries," he says. "It comes across that what they choose to do, they will do it and then expect others to follow."
That perception undermines international support for American goals, though many people in many countries share them, says Jeanne Lescure, a retired French Metro worker. "I understand that [Bush] is worried about security," she says. "We are all worried about it. But he goes about things the wrong way."
A more productive approach, suggests Karsten Voigt, a top adviser to German Chancellor Gerhard Schröder, would be to pay more attention to America's friends.
"In the end even the world superpower USA needs allies and they can't get any better ones than the Europeans," he told German radio on Wednesday. "And in order to have Europe on their side they need to keep an open ear to our arguments."
The most immediate and crucial test of such efforts, it is widely felt, will come in Iraq, now that even the fiercest opponents of the US-led invasion fear for the international fallout if Baghdad descends into civil war.
"If I could sit down with Bush, the first thing I would do is see how he could leave Iraq in a coherent fashion, with his head high and without dividing the European allies," says Catherine Durandin, an analyst at the Institute for International and Strategic Relations, a think tank in Paris.
That is a goal broadly shared in the Middle East. "This is the issue I care most about," says Sumer Said, a young Egyptian woman who stayed up all night with friends in Cairo to watch the election returns. "I want to see the American forces leave as soon as possible. But it shouldn't be immediately because then there would be chaos. The best thing the American president could do would be to set a timetable for withdrawal."
On very different issues, Latin Americans would also like to see more cooperation from Washington. In particular, they want the US to negotiate a planned free trade agreement "not as another instrument designed to benefit the USA, but rather as something to benefit the continent as a whole," says Geraldo Monteiro, who teaches at the State University of Rio de Janeiro in Brazil.
US subsidies and tariffs on products such as orange juice, steel, and grain hobble their exporters, Brazilians argue. "Brazil has great potential and I think the United States should recognize that and stop retaliating," says Ronaldo Amaral, a teacher. "Then we can export and go head to head with the US."
Trade and investment issues top people's agendas in other developing countries too. In India, for example, New Delhi is anxious to see Washington loosen up import and export regulations and resist the popular urge to punish US firms that close factories and call-centers at home to set up shop overseas.
"As far as most Indians are concerned, economic issues are more important than diplomatic issues," says Anurag Agarwali, a corporate accountant.
The same is true of Africa. "Don't give us more aid money," advises headhunter Peter Lotter as he sips a coffee in a Johannesburg mall. "Help us get more factories."
Washington could also help by expanding a US law that allows African countries making progress towards good government to export certain goods - from clothing to gum arabic - duty free to the United States. "The only way to get African governments and dictators to recognize that the day of their fiefdoms is over is by waving a big carrot in front of them," argues Raymond Louw, editor of Southern Africa report.
Beyond issues where the next US president could demonstrate his respect for global concerns rather than US interests, two eastern giants would like Washington to clarify its attitudes towards them.
One is China, whose relations with the US got off to a rocky start when Bush first took office over trade disputes, Taiwan's status, and a downed US spy plane.
"First of all, the administration should realize that China is a partner, not a competitor," says Jia Qingguo, associate dean of international studies at Beijing University. "They need to make this a strategic and consistent decision."
The other is Russia, where the government's increasingly authoritarian approach appears to have given US policymakers pause for thought. "It is time for America to decide whether Russia is a democratic market economy that could become a full partner, or whether it views Russia as something else entirely," says Mr. Kremeniuk. "On the basis of that assessment, set a strategy we can all work with."
In Western Europe, and particularly in France, the hope is that friends will not be treated as enemies. "Just because we don't agree on everything we shouldn't be classed as enemies," says Ludmilla Crestia, a French student. "Bush does not see us as an ally and I'd like him to change his mind."
In the Middle East, however, Palestinians and some Israelis would like to see the next US administration treat its friends a little more sternly. As Israeli Prime Minister Ariel Sharon prepares to pull out from Gaza, American "pressure is needed so that the withdrawal will not be from Gaza only" but from the West Bank too, says Mordechai Bloom, an Israeli bookstore owner in Jerusalem.
"No American president has given more to the Israeli rightists than Bush," complains Hafez Barghouthi, editor of the Palestinian daily Al-Hayat Al-Jadida. Now, he says, Washington should not allow Mr. Sharon to unilaterally withdraw from Gaza, and instead force him to negotiate a peace settlement with the Palestinian Authority.
It is not only the Israelis and Palestinians who need America to resolve their problems, argues Ms. Durandin, the French political analyst. Given its overwhelming power, "we all need America," she says. "And there is a great desire, all over the world, to recognize an America we can like."
• Scott Baldauf in New Delhi; Andrew Downie in Rio de Janeiro; Ben Lynfield in Jerusalem; Abraham McLaughlin in Johannesburg, South Africa; Kathleen McLaughlin in Shanghai, China; Dan Murphy in Cairo; Mark Rice-Oxley in London; Andreas Tzortzis in Berlin; and Fred Weir in Moscow contributed to this report.