KEENE, N.H. — Senators Obama and Clinton banged heads over the Iraq war yesterday, marking their first dustup since the start of the presidential campaign.

Just a day after officially announcing his candidacy in Illinois, Mr. Obama took aim at Mrs. Clinton’s vote to authorize the war, saying, “I think the war was a tragic mistake and it never should have been authorized.”

Mrs. Clinton’s vote is the one issue that has been dogging her thus far in the campaign. Otherwise, enthusiastic crowds have been giving her standing ovations on her proposals covering everything from health care to energy dependency. Mr. Obama told reporters that his early opposition to the war is proof positive that “it was possible to make judgments that this would not work out well” and that it speaks “to the kind of judgment that I will be bringing to the office of president.”

“I am not clear on how she would proceed at this point to wind down the war in a specific way,” Mr. Obama told the Associated Press in an interview. “I know that she’s stated that she thinks the war should end by the start of the next president’s first term. Beyond that, though, how she wants to accomplish that, I’m not clear on.”

A spokesman for Mrs. Clinton, Howard Wolfson, issued a statement last night in response to Mr. Obama’s comment, saying the former first lady has been a “forceful critic” of the war and has “strongly opposed President Bush’s escalation.”

“Had she been president in October of 2002, she would not have started this war and if Congress doesn’t end this war by January of 2009, as president, she will,” Mr. Wolfson said.

Yesterday’s clash came as the two Democrats were campaigning in the two most crucial early nominating states. Mrs. Clinton was here in New Hampshire wrapping up a two-day campaign swing, while Mr. Obama was stumping in Iowa and Illinois and preparing for his own trip to New Hampshire today.

At an event at Keene High School, in the southwest corner of this state, a questioner at a town hall meeting, as if on cue, asked Mrs. Clinton to pledge that she would “not put down my fellow Democrats.”

Mrs. Clinton answered with an emphatic “yes” and said a positive tone in the campaign would lead the country in a better direction. “I want to run a campaign about the future and about the issues and what I would do as president, and I would leave it to the voters to sort out the differences among us,” she told roughly 2,500 people in the gym and an overflowing auditorium. “I want to be positive and optimistic about what we can do together.” Earlier in the day, Mrs. Clinton bluntly told a group of about 50 New Hampshire residents that high-ranking Republicans are more afraid of her than of any of her opponents.

“I know what Gingrich tells people privately. I know what DeLay tells people privately. I know what Karl Rove tells people privately,” Mrs. Clinton said at a private party in Nashua in response to a question about how she would deal with Mr. Rove’s notoriously shrewd political tactics.

“I’m the one person they are most afraid of. Bill and I have beaten them before and we will again,” she declared.

She also ramped up her rhetoric on the infighting in Iraq, saying several times that America would not be left to “babysit a civil war.” A New Hampshire resident, Eric Schumacher, who attended yesterday’s event in Keene, said it would be “disingenuous for the candidates to not talk about Iraq” and draw comparisons.

“We do not have the luxury of not focusing on that,” he said as Mrs. Clinton signed copies of her book for supporters in the school’s gymnasium. “I think that at the end of the day is going to emerge as the issue.”

A business owner, Philip Huber — who was at Keene High School to see Mrs. Clinton, but was carrying a copy of Mr. Obama’s book — called it “absurd” to ask politicians to take pledges.

Mrs. Clinton stuck largely to her stump speech in Keene, talking about CEO pay, health care costs, No Child Left Behind, global climate change, and the squeeze on the middle class.

The crowd was mostly wowed, but the decision to insist that President Bush made a mistake on Iraq rather than taking that responsibility is trailing her like a bad odor. She has introduced legislation to cap troop levels at their January 1 strength and to cut off funding for Iraqi, but not American, forces. Mr. Obama has proposed starting a troop withdrawal in May. Senator Edwards, another of her Democratic rivals, has proposed pulling out 40,000 to 50,000 troops.

At a party in Manchester, a woman told Mrs. Clinton that her explanation for voting to authorize the Iraq war “doesn’t fly.”

Meanwhile, Mrs. Clinton received praise yesterday from an unexpected source. A former Arkansas governor, Mike Huckabee, told George Stephanopoulos on ABC that she is a “brilliant human being” and said Republicans “underestimate Hillary Clinton at their own peril.”

“I think people underestimate her. And I think, when they do, they’re going to be sorry,” he said. A waitress at Pappy’s Pizza in Manchester, Kelly Riley, had a similar take. After Mrs. Clinton dropped in yesterday morning, Ms. Riley predicted that New York’s junior senator would win the presidency.

“You usually know who is going to be the winner. She’s gonna win. She’s going to be the president.”