The president is scheduled to address the General Assembly Tuesday at 10:30 a.m. ET. CBSNews.com will offer a live Webcast of the address and CBS News will broadcast the event.
Still, Mr. Bush says he's not sure the United States will have to yield a significantly larger role to make way for a new U.N. resolution on Iraq. He also continued to insist on an orderly transfer of authority to the Iraqis rather than the quick action demanded by France.
"I do think it would be helpful to get the United Nations in to help write a constitution," Mr. Bush said in an interview taped Sunday with Fox News. "I mean, they're good at that."
"Or, perhaps when an election starts, they'll oversee the election. That would be deemed a larger role," he said.
In the interview, Mr. Bush said he will declare in his speech Tuesday at the U.N. General Assembly that he "made the right decision and the others that joined us made the right decision" to invade Iraq.
But the president said he will ask other nations to do more to help stabilize Iraq.
"We would like a larger role for member states of the United Nations to participate in Iraq," Mr. Bush said in the interview to be aired Monday. "I mean, after all, we've got member states now, Great Britain and Poland, leading multinational divisions to help make the country more secure."
Asked if he was willing for the United Nations to play a larger role in the political developments in Iraq to get a new resolution, Mr. Bush responded, "I'm not so sure we have to, for starters."
But he said he did think it would be helpful to get U.N. help in writing a constitution for Iraq.
Germany, France and Britain have also called for more authority for the world body in Iraq, as Washington debates with its allies over a new U.N. resolution. British Prime Minister Tony Blair, however, has not joined France's call for a quick handover of power to Iraqi, backing the U.S. stance instead.
"The key on any resolution," Mr. Bush said, "is not to get in the way of an orderly transfer of sovereignty based upon a logical series of steps. And that's constitution, elections, and then the transfer of authority."
Mr. Bush said he would tell the United Nations that while some countries did not agree with the U.S.-led military action in Iraq, it's now in the international community's best interest to not only rebuild Iraq, but rebuild Afghanistan, fight AIDS and hunger, deal with slavery and proliferation of heinous weapons.
He said the United Nations has a chance to do more as a result of U.N. resolution 1441.
The United States argues that U.N. resolution 1441, passed unanimously in November, provided sufficient authority for the U.S.-led war. That resolution threatened Baghdad with "serious consequences" if it failed to show it had handed over or destroyed its weapons of mass destruction.
"That's the resolution that said if you don't disarm there will be serious consequences," he said. "At least somebody (the United States) stood up and said this is a definition of serious consequences."
However, since the end of major combat on May 1, no proof has been reported of the allegations that Iraq had weapons of mass destruction. Both Mr. Bush and Blair have come under fire for exaggerating the threat Saddam posed.
The president's speech Tuesday will mark a return to the podium where the public push toward war began. There, on Sept. 12, 2002, Mr. Bush challenged the United Nations to act in Iraq.
Months later, the quest for international backing for war ended there as well, when the U.S., Britain and Spain withdrew a resolution backing force because it was clear that it would lose a Security Council vote or be vetoed by France.