In a veiled barb at US President George Bush who was in the audience, Annan on Tuesday cited Iraq's post-war chaos and the prisoner abuse scandal among "flagrant and topical" examples of disregard for fundamental laws.
"It is by rigorously upholding international law that we can and must fulfil our responsibility to protect innocent civilians from genocide, crimes against humanity and war crimes," Annan said as he began the UN General Assembly session.
A week after he had agreed in an interview that the US-led invasion of Iraq was illegal, Annan's address was largely seen as another dig at the United States.
"History will judge us very harshly if we let ourselves be deflected from this task or think we are excused from it by invocations of national sovereignty," he said.
Besides Iraq, the UN chief's address also touched on the crisis in Darfur, the Russian school hostage tragedy and the Israeli-Palestinian crisis.
Annan was critical of the chaos
in post-war Iraq
"In Iraq, we see civilians massacred in cold blood while relief workers, journalists and other non-combatants are taken hostage and put to death in the most barbarous fashion," he said.
"At the same time, we have seen Iraqi prisoners disgracefully abused," he added.
Annan also repeated a warning he gave the assembly last year that the UN was at a "fork in the road" after the US decision to go to war without full backing from the Security Council.
"More than ever, the world needs an effective mechanism through which to see common solutions to common problems. That is what this organisation was created for," he said.