President Obama has told British politicians that, despite the rise of new global powers, the time for US and European leadership "is now".
He said the influence of the US, UK and allies would remain "indispensable," in a speech in Parliament on the second day of his UK state visit.
But he said that leadership would need to "change with the times" to reflect economic and security challenges.
He is the first US president to address MPs and peers in Westminster Hall.
Rows of the UK's most senior politicians and other prominent figures lined the historic building to hear the US president talk about the history of the UK's relationship with the United States and its shared values - and outline some of the future challenges facing the world.
Former British prime ministers Sir John Major, Tony Blair and Gordon Brown sat next to each other in the packed hall - the oldest part of the Houses of Parliament - which fell silent as the US president began his 35-minute speech.
As he began, Mr Obama joked that with an "especially active press corps", the relationship between the UK and US was forever being "over analysed".
But he added: "There are few nations that stand firmer, speak louder and fight harder to defend democratic values around the world than the United States and the United Kingdom."
He said the two countries had "arrived at a pivotal moment once more" following global recession and years of conflict.
With the winding down of operations in Iraq, progress in Afghanistan and having dealt "al-Qaeda a huge blow by killing its leader Osama Bin Laden", President Obama said it was time to enter a "new chapter in our shared history" with new challenges.
But he rejected arguments that the rise of superpowers like China and India meant the end for American and European influence in the world.
"Perhaps, the argument goes, these nations represent the future, and the time for our leadership has passed. That argument is wrong. The time for our leadership is now," he said.
"It was the United States, the United Kingdom, and our democratic allies that shaped a world in which new nations could emerge and individuals could thrive.
"And even as more nations take on the responsibilities of global leadership, our alliance will remain indispensable to the goal of a century that is more peaceful, more prosperous and more just."
But he added that leadership had to "change with the times" and the days were gone when an American president and UK prime minister could "sit in a room and solve the world's problems over a glass of brandy".
BBC News - President Obama: Now is time for US and West to lead
I think Obama is wrong to say West still leads the world, as China and Japan and India are top 10 economies in the world.