The secretary-general symbolically traveled to the Truman Presidential Museum and Library in Independence, Missouri, to make his final major speech in office.
Addressing a crowd that included politicians and academics, he praised the late president Truman's efforts to help rebuild Europe after World War Two.
Although the secretary-general did not name the Bush administration, he made it clear he was not satisfied with the current U.S. leadership.
"You Americans did so much, in the last century, to build an effective multilateral system, with the United Nations at its heart. Do you need it less today, and does it need you less, than 60 years ago? Surely not. More than ever today, Americans, like the rest of humanity, need a functioning global system, through which the world's peoples can face global challenges together. And, in order to function, the system still cries out for far-sighted American leadership, in the Truman tradition."
Mr. Annan cautioned Washington not to abandon its ideals as it carries out the fight against global terrorism.
"This country has historically been in the vanguard of the global human rights movement. But that lead can only be maintained, if America remains true to its principles, including in the struggle against terrorism. When it appears to abandon its principles, including in the struggle against terrorism. When it appears to abandon its own ideals and objectives, its friends abroad are naturally troubled and confused."
Mr. Annan repeatedly invoked Harry Truman's name, and singled out the United States in urging nations to, in his words, "do the right thing," and "play by the rules."
"The U.S. has given the world an example of a democracy in which everyone, including the most powerful, is subject to legal restraint. Its current moment of world supremacy gives it a priceless opportunity to entrench the same principles at the global level. As Harry Truman said, 'We all have to recognize, no matter how great our strength, that we must deny ourselves the license to always do as we please.'"
Following the speech, Mr. Annan rejected a questioner's suggestion that his comments were an attack on U.S. foreign policy. He said "nothing could be further from the truth."
He said the address should be interpreted as a call for U.S. leadership.
"What I'm saying here is that, when the U.S. works with other countries in a multilateral system, we do extremely well. We need U.S. leadership. The U.S. provided that leadership in the past, and our world is in a sorry state. We have lots of problems around the world, and we require the natural leadership role the U.S. played in the past, and can play today."
Mr. Annan has several times been sharply critical of U.S. positions, and has had a rocky relationship with Washington's U.N. Ambassador John Bolton.
President Bush invited the secretary-general and Bolton to a private dinner last week at the White House. When asked about the mood at the affair, Bolton suggested it had not been warm.
Mr. Annan and Bolton will both be leaving their posts within the next few weeks. The secretary-general will be succeeded by the former South Korean foreign minister Ban Ki-Moon. No replacement has yet been named for Bolton.