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CONCORD, N.H. — For the fourth time in her career — as a political spouse and as a presidential candidate — Hillary Rodham Clinton made her way into the crowded and crusty office of New Hampshire’s secretary of state as the Clinton surname was placed on the ballot for the state’s primary, the first in the nation.

“You know this is my fourth time,” Mrs. Clinton said as she sat down to take questions from the local news media at the New Hampshire Statehouse. “I came in December of 1991 to officially sign the papers on behalf of my husband’s campaign, and it was a far different scene than this one because there were very few people who gave him much of a chance,” Mrs. Clinton said.

Realizing she had little to gain by attacking her rivals — Democrat or Republican — Mrs. Clinton demurred when asked about Senator Bernie Sanders of Vermont and Ben Carson. Asked why Donald J. Trump had higher ratings for his “Saturday Night Live” stint than she did, she said: “Consider the performance.”

Mr. Sanders has faced criticism recently from Democrats for his political status as an independent and what some consider his wavering support of President Obama, who is widely popular among Democratic primary voters.

“I’ve been a Democrat for a very long time,” Mrs. Clinton said, without directly responding to a question about whether her main rival is a loyal Democrat. “I’ve supported a lot of Democrats over the years,” Mrs. Clinton continued. “As president, I’d tell a lot of Democrats across the country that I want to help build the party from the ground up.”

As elected officials coalesce behind Mrs. Clinton’s candidacy, so did a major environmental group — The League of Conservation Voters, which endorsed Mrs. Clinton at a small gathering in Nashua on Monday, giving her a major boost from a liberal group that for a while appeared poised to potentially endorse Mr. Sanders.

Rather than playing up what the endorsement means for her primary battle, Mrs. Clinton used the nod to pivot to attack the Republican presidential candidates.

“In 2008, the Republican Party platform had a long section about climate change,” she said. “And now we have candidates like Ted Cruz who say climate change is not science,” Mrs. Clinton continued. “That can be pretty dispiriting, but it can also be galvanizing.”

After months of tight polls in New Hampshire before Mr. Sanders appeared to surge ahead, Mrs. Clinton has seen her poll numbers there improve. On Monday, the campaign introduced an ad in the state and in Iowa that promotes Mrs. Clinton’s college affordability plan, a proposal that is popular in states where college debt is a major issue.

After the Nashua event, Mrs. Clinton headed to a town-hall-style meeting in Windham to field questions from voters. On Tuesday, she was scheduled to unveil a plan to help veterans at a round-table discussion and speak at a business group’s dinner.