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Bush speaks to the General Assembly at 10:30 a.m. ET.

National security adviser Condoleezza Rice said Bush is insistent that a transfer of power to Iraqis must be "an orderly process" and come only after free elections.

"The French plan, which would somehow transfer sovereignty to an unelected group of people, just isn't workable," she told reporters.

France favors a two-stage plan for Iraqi self-rule. The first step would be a symbolic transfer of sovereignty from U.S. hands to the current Iraqi Governing Council, a 25-member body appointed by U.S. authorities. That would be followed by a gradual ceding of power over six to nine months.

The United States wants to hand over power only after the council produces a constitution, has it ratified by the Iraqi people and conducts elections.

Bush's objective in his speech and in one-on-one meetings with other leaders is a Security Council resolution that paves the way for more international troops and financial aid but retains U.S. management of the military effort. Among those he'll meet with are two of the Iraq war's most vocal opponents: French President Jacques Chirac and German Chancellor Gerhard Schroeder.

Bush will try to convince his counterparts that despite setbacks, significant progress is being made in stabilizing Iraq. He will say that it is in the interest of world peace for the international community to help bring about stability and democratic government there as quickly as possible.

Bush met in the Oval Office on Monday with two ministers from Iraq's temporary government and declared that "good progress" has been made. But his case suffered a setback with a suicide bombing at the U.N. compound in Baghdad. The attack, which killed a guard, came a month after a truck bombing at the compound killed 23.

U.N. Secretary-General Kofi Annan voiced alarm at the level of security in Baghdad. "We need a secure environment to be able to operate," Annan said. "We will go forward, but of course if it continues to deteriorate, then our operations will be handicapped considerably."

Annan has been an important advocate of an Iraq resolution, but he expressed the mood of many U.N. members Monday when he told an anti-terrorism conference in New York that force alone would not win the battle against extremist violence.

"To fight terrorism, we must not only fight terrorists. We have to win hearts and minds," he told the gathering of 18 heads of state.

In his prepared address for today's meeting, Annan will call on the international community to take "the extra time and patience" to reach a consensus on Iraq that is "coherent and workable" — and to use the same process of deliberation to resolve the other global crises confronting the world.

"Let me reaffirm the great importance I attach to a successful outcome in Iraq," Annan's speech says. "Subject to security considerations, the United Nations system is prepared to play its full part in working for a satisfactory outcome in Iraq, and to do so as part of an effort by the whole international community."

Nichols reported from the U.N., Benedetto from Washington. Wire reports