Hillary Rodham Clinton announced today that she definitely will be a Senate candidate in New York and that she intends to scale back her duties as first lady so she can move to the state and campaign "as vigorously as possible."

Clinton acted to put to rest mounting speculation that she would decide against running, after a series of missteps that wounded her candidacy and polls that show her facing an increasingly competitive race against New York Mayor Rudolph W. Giuliani, the likely Republican candidate. "I intend to run," she told supporters here. Clinton said she would make her formal announcement early next year.

Clinton said she would be taking up residence in the house in Chappaqua that she and President Clinton recently purchased. "I'm going to be moving into my house as soon as the Secret Service tells me that it's ready and available to be moved into. Obviously, I will still be in Washington from time to time. I have to be. There are many things that I will still have to tend to. But I will be living in Westchester and I'll be traveling around the state and campaigning."

Clinton's announcement, which came during a campaign event before the United Federation of Teachers, seemed intended to reassure the party faithful, not to mention contributors, that she was not going to back out.

In what appeared to be an orchestrated question, the union's president, Randi Weingarten, asked: "Is it yes or is it no?"

Clinton took the long road to her short answer. "You know, Randi, in the past months I have been--at last count--in at least 35 counties all over this state, and everywhere I've gone people talk to me about issues like what we've discussed today. And that's very exciting to me because I believe that if we work together we really can make a difference for the children and families of New York. So, the answer is: Yes. I intend to run."

The audience of educators burst into cheers as the downtown union meeting room became the unexpected backdrop for an unprecedented but troubled campaign's attempt to buoy itself.

The announcement comes after the rockiest period of Clinton's campaign, when key Democrats here publicly questioned whether she is up to the task of running against the New York mayor, and several even suggested she not run. Critics have decried, among other things, the campaign's lack of a full-time manager. But sources close to Clinton said last week that she has selected a campaign manager, Bill de Blasio, the Department of Housing and Urban Development's top official in New York, though she has not publicly announced it.

In the latest campaign misstep, Clinton appeared to have damaged her support among a core Democratic constituency--New York Jews--many of whom questioned her handling of Middle East issues. And some Democratic officials who have been shepherds of her campaign began publicly prodding her to roll up her sleeves, stop acting like a first lady, and get more focused on this pivotal and expensive Senate campaign. State Democratic Party Chairman Judith Hope recently told the first lady to "give up her day job."

Recent polls show Clinton slightly behind Giuliani or at best in a statistical dead heat. That is a far cry from her early leads last spring, when her exploratory campaign glowed with the patina of political celebrity.

A spokesman for Giuliani's campaign, Bruce Teitelbaum, called Clinton's comments today "a non-announcement."

"What happened today was an announcement about a press conference to announce that Mrs. Clinton intends to announce next year," Teitelbaum said.

Although neither candidate has officially announced, both have been running television commercials. In addition, an ad paid for by a Republican group began airing this week criticizing Clinton for silently sitting by while Suha Arafat, wife of the Palestinian leader, used the first lady's Nov. 11 visit to the West Bank as the occasion to deliver a tirade against Israel, including the unsubstantiated claim that Israel uses "poison gas" that causes high cancer rates among Palestinians.

Clinton explained today, as she has before, that she made no immediate comment on Arafat's remarks because she believed it was improper to potentially upset the delicate peace talks between the Israelis and Palestinians. "I know that there are some here in New York who wish that I had created some sort of international incident when I was abroad," she said. "But that would not be useful for the peace process."

But as if to acknowledge that this flap arose because of the untenability of her dual roles as first lady and candidate for public office, she said she will make changes. Starting with the new year, she said, she will scale back her duties as first lady "so that I would be free to campaign as vigorously as possible, which I intend to do."

She said she had not told her husband and daughter, who are in Kosovo, of today's announcement, adding, "But they're getting home tonight and I don't think my husband or my daughter will be surprised."

Underscoring her new level of engagement in the Senate race, she was scheduled to give interviews to two local TV stations tonight. And for the first time in a public event, Clinton uttered Giuliani's name, departing from her vague past references to "my opponent" and "the other side." In response to a question, she said: "Ultimately this election is not going to be about me or Rudy Giuliani. It's going to be about the issues that concern the people of New York."

She even said there would be some New York City issues that she would speak out on during the campaign. "This is going to be a very hard-fought campaign," she said. "I have absolutely no illusions about it. . . . I think a hard-fought campaign about the issues that concern the people of New York is what the people of New York deserve to have."

CAPTION: "I intend to run," Hillary Clinton told a New York teachers group, adding she will move into new house soon.

CAPTION: Hillary Clinton listens to a question at a New York news conference after her campaign announcement.