President Bush, facing increasing pressure to articulate an exit strategy for Iraq, said on Tuesday that "it would be a terrible mistake" to pull U.S. troops out of the country until a path to victory is secured.

But signaling the likely start next year of a substantial reduction in U.S. forces in Iraq, Defense Secretary Donald H. Rumsfeld said "it's time" for Iraqi troops to assume more responsibility for their country's security.

The remarks by the president and his top defense official came ahead of a speech that Bush is due to give Wednesday at the U.S. Naval Academy in Annapolis aimed at more fully outlining his Iraq strategy. The speech has been billed by officials as the first in a series of events that Bush will hold to spotlight progress in Iraq and to lay out U.S. intentions before the Dec. 15 elections for a new Iraqi government.

Bush's approval rating has slipped to the lowest point in his presidency, as the U.S. death toll in Iraq has surpassed 2,100 and public sentiment has swung decidedly against the war. That mood has affected Congress, where earlier this month the Senate passed a measure requiring the administration to advise it more closely on its Iraq strategy.

In recent days, administration officials have joined senior military officers in raising expectations of a significant reduction in U.S. troops after the Iraqi vote. Although the Iraqi insurgency shows little sign of waning, the country's new homegrown security forces have taken over enough of the fight to permit a partial drawdown of U.S. forces, according to U.S. military commanders.

At the same time, senior military officers have made clear their opposition to a quick withdrawal, saying that such a move would threaten many strategic gains made over the past 21/2 years and could trigger the collapse of Iraq's fledgling national army.

The Pentagon has already announced plans to reduce the number of U.S. troops in Iraq after the Dec. 15 elections, from 155,000 to 138,000, their base level during most of this year. U.S. commanders have privately indicated that further near-term reductions are likely, although no announcement is expected until after the Iraqi vote. The plans call for an additional cut of about 10,000 troops by holding back two of 17 Army combat brigades scheduled to rotate into Iraq.

Speaking to reporters after touring the U.S.-Mexican border here, Bush said that his decision to pull forces out of Iraq will be based on the ability of Iraqi security forces to carry the fight against the raging insurgency and not on politics.

"I want to defeat the terrorists, and I want our troops to come home," the president said. "But I don't want them to come home without having achieved victory."

Bush also took time to address critics who say he should set a clear timetable for withdrawing troops from Iraq.

"Now I know there's a lot of voices in Washington," he said. "We've heard some people say, 'Pull them out right now.' That's a huge mistake. It'd be a terrible mistake. It sends a bad message to our troops. And it sends a bad message to our enemy, and it sends a bad message to the Iraqis."

At the Pentagon, Rumsfeld also warned about the risks of a quick U.S. withdrawal from Iraq.

"Quitting is not an exit strategy," he said in opening remarks at a news conference. "It would be a formula for putting the American people at still greater risk. It would be an invitation for more terrorist violence.

"Rather than thinking in terms of an exit strategy, we should be focused on our strategy for victory," he added.

But Rumsfeld also stressed that the Iraqis are able to assume greater responsibility for their own security and that the time has come for them to do so.

His comments reflected the sensitive balancing act that confronts the administration as it starts to lay the public groundwork for a withdrawal of U.S. forces while continuing to argue that a sustained American military presence is needed in Iraq.

On one hand, U.S. officials and military commanders are eager to make the case that there has been sufficient progress in the country to justify a drop in the U.S. troop level. On the other, they want to avoid raising expectations that the U.S. military's mission in Iraq is ending and that all forces will be out within a year or two.

Any troop cut also runs the risk of renewed criticism from such influential defense experts as Sen. John McCain (R-Ariz.), who have argued that the United States does not have sufficient forces to hold territory cleared of insurgents and should increase, not decrease, its military presence in Iraq.

Asked about this argument, Rumsfeld bristled, saying that Iraqi forces should be the ones responsible for securing strategic gains and ensuring the reconstruction of the country.

"They have to do it for themselves," Rumsfeld said. "There isn't an Iraqi that comes into this country and visits with me that doesn't say that. They know that. They know that they're the ones that are going to have to grab that country. And it's time."

Looking ahead to the Dec. 15 vote, Rumsfeld declined to go so far as to predict that it will mark a decisive "tipping point" away from violence and toward greater stability. But he said that he sees "more positive things taking place than negative things" in Iraq and asserted that the insurgency will get weaker next year.

Graham reported from Washington.

President Bush, with Border Patrol officer Paul Beeson and Gov. Rick Perry, said: "I want to defeat the terrorists, and I want our troops to come home."