Archbishop Desmond Tutu has warned Barack Obama of the risk of squandering the goodwill he says the US president's election has generated.
In an article for BBC News, he says it would be "wonderful" if Mr Obama apologised for the invasion of Iraq.
He also says he prays that Mr Obama will be tough on African dictators.
The Nobel Peace Prize winner adds that the UK's standing in the world has suffered because of its co-operation with the US in the "war on terror".
'Dance and shout'
In the exclusive article for BBC News, based on a lecture he will give in London on Thursday to mark the 75th anniversary of the British Council, the former Archbishop of Cape Town speaks of his joy at watching the US election results coming in.
"I wanted to jump and dance and shout, as I did after voting for the first time in my native South Africa on 27 April 1994."
He calls Mr Obama's election an "epoch-making event that filled the whole world with hope that change is possible".
However, he also sounds a note of caution.
He reminds his readers of the outpouring of sympathy that followed 9/11 and how quickly it vanished in the light of the allegations of prisoner abuse at Abu Ghraib and Guantanamo Bay.
"Obama, too, could easily squander the goodwill that his election generated if he disappoints," he says.
He adds: "It would be wonderful if the US president could apologise for the US-led invasion of Iraq on behalf of the American people."
He urges the president and the Secretary of State, Hillary Clinton, to act quickly to reach out to other countries, to build bridges with them and to listen to what they say.
Pointing to the inspirational role of the US during the struggle against apartheid, the veteran campaigner for reconciliation asks President Obama to "come down hard" on African dictators.
The archbishop says November's election has turned America's image on its head after what he says were seven lean years for those who looked to America for inspiration.
"The Bush Administration managed to rile people everywhere. Its bully-boy attitude sadly polarised our world," he says.
But Desmond Tutu is also critical of the role of the British government in the so-called war on terror.
He says the country's standing has been damaged as a result of its close co-operation with the US and that it lacks what he calls the "redeeming Obama factor" to restore the UK's perception abroad.
The archbishop also has some positive words for Britain, and the British Council in particular.
He praises its work in helping the government of Nelson Mandela reform the post-apartheid diplomatic service and train black teachers.
Martin Davidson, chief executive of the British Council, said: "It is particularly appropriate that Archbishop Desmond Tutu has opened our 75th anniversary lecture series.
"This is also a testament to the long-lasting ties that can be built through cultural relations. We worked in South Africa during the apartheid years, building the foundations for future cooperation and collaboration."