Prime Minister Gordon Brown has urged a "new dawn" in co-operation between Europe and the US.
All European leaders could work with the US to forge "stronger transatlantic links", he said in a speech in Boston on the last day of his US trip.
He urged them to work together to reform institutions like the UN, World Bank and International Monetary Fund.
They needed reforming to meet modern challenges, he told an audience at the John F Kennedy Presidential Library.
"The tantalising possibilities of a world where as John F Kennedy put it, the strong are just, the weak secure and the peace preserved are matched only by the terrifying risks of us failing to seize this moment"
Mr Brown, who is said to be angry that his trip to the US has been overshadowed by rows at home over his tax reforms, wants the UN to become more effective in conflict prevention and resolution.
He also wants the IMF to develop as an early warning system to prevent problems like the global credit crunch and the World Bank to acquire a new environmental emphasis.
He said: "Now is an opportunity for an historic effort in co-operation; a new dawn in collaborative action between America and Europe - a new commitment from Europe that I believe all European leaders can work with America to forge stronger transatlantic links.
"For I sense common ground between our two great continents in the urgent need for renewal and reform."
'Truly global'
Continuing this theme, he called for "strong regional organisations, building up the African Union as we built up the European Union".
Ultimately, he called for established institutions to "bring to a troubled world the humanitarian and peacekeeping and the support for stability and reconstruction that has been absent for too long", all of which would be "built around the vision of a global society founded on revitalised international rules and institutions".
He also said that emerging nations such as China, India, South Africa and Brazil should have a greater influence in organisations like the G8, the IMF and the World Bank.
"We have the opportunity to come together around a global covenant to reframe the international architecture "
"Today - as we face these new global challenges - the tantalising possibilities of a world where as John F Kennedy put it, the strong are just, the weak secure and the peace preserved are matched only by the terrifying risks of us failing to seize this moment," he said.
"For the first time in human history we have the opportunity to come together around a global covenant to reframe the international architecture and build the truly global society."
Mr Brown has met President Bush and the three presidential candidates, senators John McCain, Hillary Clinton and Barack Obama in private meetings during his three-day trip.
Tax protests
But it has been overshadowed in the US media by that of Pope Benedict XVI, and he is said to believe a row over his decision to abolish the lowest rate of income tax at home has been exaggerated by the UK media.
On Thursday he broke off from meetings to telephone Labour MP Angela Smith to persuade her not to quit as a ministerial aide over the issue.
Later Ms Smith issued a statement denying she was about to quit as a parliamentary aide to Treasury Chief Secretary Yvette Cooper.
But since then four more ministerial aides have joined protests at the abolition of the 10p tax rate - although none have threatened to resign.
In total more than 70 Labour MPs have signed one of three motions protesting about the tax move, which came into force this month.
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