"We must form new alliances, based on these common values; ones not just to protect us from the world but ones which reach out to the world. A new alliance of opportunity," he said the a speech at the US-based Council on Foreign Relations.
He said that while there were few global challenges that did not require US engagement, countries should work together through organisations like the United Nations to seek shared solutions to the world's problems.
Washington has been watching the new government of Gordon Brown, the British prime minister, for signs of any foreign policy change after years of close ties under his predecessor Tony Blair.
The Guardian newspaper said the speech contained the "the first clear signs" that Brown would reorder Britain's foreign policy.
While, The Times described it as "a series of coded criticisms of American foreign policy".
Brown took over the premiership last month, promising to bring voters back to the ruling Labour Party and draw a line under the unpopular war in Iraq.
Few analysts expect Brown to announce an immediate withdrawal of British troops from Iraq, but there is speculation the pull out may accelerate.
Britain has been reducing troop numbers in Iraq and currently has about 5,500 in the south.
Alexander is a close ally of Brown who gave him his first political job as a parliamentary researcher and speechwriter.
Later he said in an interview with BBC radio: "Gordon Brown has made very clear that he regards a strong relationship with the US as being one of the fundamental bases of his foreign policy.
"But he also wants to see strong relationships with our partners within the European Union, and indeed growing and strong relationships with China and India, emerging powers in Asia."