Making his last address as secretary-general, Annan said the past decade had seen progress in development, security and the rule of law - the three challenges he said humanity faced in his first address to the General Assembly in 1997.
But Annan said too many people were still exposed to brutal conflict, the fear of terrorism had heightened religious tensions, terrorism was being used to limit or abolish human rights, and globalization risked driving apart the rich and poor.
"The events of the last 10 years have not resolved, but sharpened, the three great challenges I spoke of - an unjust world economy, world disorder, and widespread contempt for human rights and the rule of law,"Annan said.
"As a result, we face a world whose divisions threaten the very notion of an international community, upon which this institution stands."
Yet, Annan said, this was happening at a time when "more than ever before" people around the world had come together to face global challenges, such as AIDS and the environment.
"I remain convinced that the only answer to this divided world must be a truly United Nations," he said.
In his annual report, Annan touched on some of the most difficult issues confronting the leaders from countries large and small assembled in front of him.
He said the Arab-Israeli conflict is the most potent and emotionally charged conflict in the world today.
"As long as the Palestinians live under occupation, exposed to daily frustration and humiliation, and as long as Israelis are blown up in buses or in dance halls, so long will passions everywhere be inflamed,"Annan said.
Annan also lamented the continuing conflict in Sudan's western Darfur region, saying "the continued spectacle of men, women and children driven from their homes by murder, rape and the burning of their villages makes a mockery of our claim, as an international community, to shield people from the worst abuses."
Reports surfaced of a possible military coup in Thailand during Annan’s speech. The UN spokesman's office announced soon after that Thaksin Shinawatra, Thai prime minister, would speak to the General Assembly on Tuesday night instead of early Wednesday afternoon, due to the events.