Bush renewed attacks on Iran.
In a speech to almost 90 world leaders in New York, Bush also defended American involvement in the Middle East, just hours before a much-awaited speech by Iran's President Mahmoud Ahmadinejad.
Mr Bush used the speech to appeal directly to the people of the Middle East and answer critics of his promotion of democracy in the region.
"Extremists in your midst spread propaganda claiming that the West is engaged in a war against Islam. This propaganda is false, and its purpose is to confuse you and justify acts of terror,” he said.
“We respect Islam, but we will protect our people from those who pervert Islam to sow death and destruction. Our goal is to help you build a more tolerant and hopeful society that honours people of all faiths and promote the peace."
Iran under fire
Mr Bush also renewed his attack on Iran, accusing it’s rulers of sponsoring terrorism and trying to pursue nuclear weapons, but vowing to find a diplomatic solution to the crisis.
French President Jacques Chirac has put forward a compromise plan after meeting with the US President in a bid to ease tensions without resorting to sanctions.
Under the proposal, Iran and the six major powers involved in the stand-off
would agree on "an agenda" for broad negotiations on economic and diplomatic relations between the West and Iran.
If it succeeds it will represent the first formal contact between Tehran and the United States in 27 years.
Middle East debate
However the first day of the debate by world leaders was marked by renewed calls to end the Israel-Palestinian conflict.
Mr Annan, making his final speech to a General Assembly after 10 years as UN secretary general, singled out the Israeli-Palestinian conflict as one of the most important security challenges facing the world.
"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," he said.
He warned that failure by the UN Security Council to end the nearly 60-year-old conflict would lead to declining respect for the United Nations.