“No nation can make itself secure by seeking supremacy over others,” Mr Annan said, urging the US to respect human rights in its “war on terror”.
Mr Annan said states had to be accountable and the UN was the only body where this could be assured.
The speech has been interpreted as a sharp rebuke of President Bush.
Our correspondent in Missouri, Jonathan Beale, said Mr Annan again raised objections to the Iraq war, a war he has already condemned as illegal.
“When power, especially military force, is used, the world at large will consider it legitimate only when convinced that it Is being used for the right purpose - for broadly shared aims,” he said.
Read the speech