This may be the biggest global summit ever with leaders from around the world meeting on the 60th anniversary of the United Nations.
Fighting world poverty and ways to reform the U.N. are supposed to be the focus of the summit, which is taking place as a new General Assembly session gets underway.
But President Bush has other matters he wants to bringto the fore. They include fighting terrorism, boosting world trade, and stopping the spread of nuclear weapons.
In his speech, the president is likely to bring up the threat posed by the nuclear ambitions of Iran and North Korea. And in his discussions on the sidelines of the summit, he is urging support for a strong international stand.
A few hours after his arrival in New York, he met with China's President Hu Jintao. The meeting took place as six party talks resumed in Beijing on Pyongyang's nuclear program. Speaking through an interpreter, the Chinese leader promised to press for progress in the negotiations.
"We stand ready to step up our communication and cooperation with the United States so we can facilitate fresh progress in the second session of the fourth round of the six party talks."
President Hu also pledged action to ease China's trade imbalance with the United States. He said China is willing to take measures to increase imports from America and cut its hugetrade surplus- which hit $17.7 billion in July.
"There is no denial that our bilateral trade has developed so fast and to such a large scale it is inevitable that we may have some friction."
Hu Jintao made no specific mention of Iran, and international efforts to convince Tehran to abandon nuclear projects that could have military uses. Earlier in the day, President Bush said he would be discussing the matter with the leaders of other countries with permanent seats on the U.N. Security Council.
Mr. Bush did not directly threaten sanctions, but said he wanted to discuss the possibility of punitive action if necessary. He stressed the stakes are high.
"It is very important for the world to understand that Iran, with a nuclear weapon, will be incredibly destabilizing. And, therefore, we must work together to prevent them from having the wherewithal to develop a nuclear weapon."
President Bush said he would also bring up the matter when he meets Wednesday in New York with British Prime Minister Tony Blair and in Washington on Friday with Russian President Vladimir Putin.