President Bush on Wednesday pushed back against John Kerry's (search) criticism of his handling of Iraq, saying, "I know what I'm doing when it comes to winning this war."

Bush used an re-election rally to sharply reject the Democratic challenger's proposal to begin to withdraw troops from Iraq within six months of taking office.

"We all want the mission to be completed as quickly as possible. But we want the mission completed," the president said. "The mission is not going to be completed as quickly as possible if the enemy thinks we will be removing a substantial number of troops in six months."

Military commanders should be deciding troop levels, Bush said.

"I know what I'm doing when it comes to winning this war, and I'm not going to be sending mixed signals," he said.

Kerry spokesman Phil Singer said Bush will "say or do anything to avoid a discussion about his failed policy in Iraq."

"One thing we know for sure is that the troops are going to be in Iraq for a lot longer under George Bush (search) than they will be with John Kerry as president," Singer said.

Bush also responded to rising criticism, some from fellow Republicans like Nancy Reagan (search), of his decision three years ago this week to cap federal funding for stem cell studies. Reagan has lobbied for more government funding for the research, which she says could yield a cure for Alzheimer's.

The president said he would not relax his policy, though he acknowledged that it is "sad" when parents believe a cure for their children's ailments could be within reach.

"The policies I made were on the one hand trying to help as best as we can move science forward, and at the same time keep an ethical balance so that we promote a culture of life," Bush said.

"The decision I made, in my judgment, was the right decision," he said.

Bush's remarks came at the start of a campaign swing through New Mexico and Arizona, two states he and Kerry have been contesting most fiercely. He lost New Mexico by just 366 votes and Wednesday marked his eighth trip.

After showing Sen. John McCain (search), R-Ariz., his Texas ranch Wednesday morning, Bush headed out for a second day of campaigning with the war hero and one-time Bush rival. McCain did not say anything at the New Mexico rally, in contrast to their trip through Florida Tuesday, where he introduced Bush at each stop.

The two men then went to Arizona, which Bush narrowly won in 2000.

McCain revved up his hometown crowd in Phoenix, telling a Bush rally that "because of what we did in Iraq, the world is safer and America is safer."

"President Bush has not wavered, he will not waver," McCain said. "We will win this war on terror."

In New Mexico, Bush spoke in one of his favorite campaign forums, which the White House bills as a town hall forum and calls "Ask President Bush."

The president roamed a square about the size of a boxing ring inside an aircraft manufacturer. One jet was left on the plant's floor, its nose pointing straight at Bush. Bush joked that he and McCain, both former fighter pilots, would take the plane out for a spin.

The event allowed fervent Bush backers to ask the president questions. But in keeping with Bush's custom, most of the event was devoted to a speech by Bush and then to testimonials from people hand-picked by the White House extolling the virtues of his policies.

The queries put to Bush in the question-and-answer session were never hard-hitting, and were often not questions at all.

Sample questions on Wednesday:

— Can I take a picture with you?

— Can I introduce you to my wife and mother in law?

— I want you to know that I'm praying for you.

When several of Bush's questioners predicted he would win re-election in a landslide, Bush said he'd be happy to win narrowly. "Let's win the thing. Let's just win it," he said.