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Senator Bernie Sanders is breaking away from Hillary Clinton in New Hampshire and is edging ahead of her in Iowa, according to new polls that show him solidifying the support of Democrats ahead the first two 2016 presidential primary election contests.

The polls add to mounting pressure on Mrs. Clinton, who was seen for months as an overwhelming favorite in the race, to avoid another upset from an insurgent Democratic challenger after her 2008 loss to Senator Barack Obama for the party’s nomination.

A survey from Quinnipiac University found that 49 percent of likely Democratic caucusgoers in Iowa are planning to back Mr. Sanders while 44 percent support Mrs. Clinton. The results represent a shift from a month ago, when the former secretary of state was leading Mr. Sanders by 11 percentage points. The poll has a margin of error of plus or minus four percentage points.

“Iowa may well become Senator Bernie Sanders’s ‘Field of Dreams,’” said Peter A. Brown, director of the Quinnipiac poll. “After three months of Secretary Hillary Clinton holding an average 10-point lead among Iowa Democrats, the playing field has changed.”

The Vermont senator has been gaining ground on Mrs. Clinton in recent polls and capitalizing on a lack of enthusiasm for her candidacy less than three weeks before the Feb. 1 Iowa caucuses. The Quinnipiac poll found that Mr. Sanders is seen as more honest and empathetic than Mrs. Clinton, and stronger on climate change and the economy. She is viewed as being more electable in a general election and stronger on foreign policy.

Gender is also turning about to be a significant factor in how the candidates are performing, with men preferring Mr. Sanders by a margin of 61 percent to 30 percent. Women back Mrs. Clinton by a margin of 55 percent to 39 percent.

A separate survey from Monmouth University, released on Tuesday, shows Mr. Sanders leading Mrs. Clinton by a margin of 53 percent to 39 percent. The poll has a margin of sampling error of plus or minus five percentage points.

The results signify a significant shift in the New Hampshire race, as Mrs. Clinton had a narrow advantage over Mr. Sanders there in a November poll from Monmouth. A Wall Street Journal/NBC News/Marist poll released this week showed Mr. Sanders with a four-percentage-point lead there.

Perhaps more worrying for Mrs. Clinton is the finding that a majority of New Hampshire voters said that their choice is set, while only 35 percent were completely decided two months ago.

“New Hampshire Democratic preferences are getting baked in, with Sanders gaining the upper hand,” Patrick Murray, director of the Monmouth University Polling Institute, said in a statement. “The final question will be who does a better job at turning out their respective voting blocs.”

Mr. Sanders is now leading Mrs. Clinton among all the major voting blocs in New Hampshire. According to Tuesday’s survey, he has overtaken her with female voters — a core constituency for the former secretary of state who would be the first female president. And he is also leading her among independent voters and with registered Democrats.

With his message of fighting to reduce income inequality and taking on Wall Street, Mr. Sanders continues to be the candidate of choice for younger voters in New Hampshire. But he has also managed to broaden his appeal since November, overtaking Mrs. Clinton with voters who are over age 50.

Lagging the two top candidates is Martin O’Malley, the former Maryland governor. His support sits at 5 percent in New Hampshire and 4 percent in Iowa, according to the new polls. But with the race tightening, his supporters could become a determining factor if they shift toward Mr. Sanders or Mrs. Clinton.