NEW YORK - Mayor Rudolph Giuliani, citing concerns about treatment for prostate cancer and beleaguered by personal difficulties, dropped out of the US Senate race yesterday, ending what was shaping up as the year's most dramatic political battle.
His departure leaves the Democratic candidate, Hillary Rodham Clinton, in an uncertain position. She looked tense, if not gloomy, when she appeared at a union headquarters shortly after the mayor's announcement to wish him well.
On one hand, Giuliani was the feistiest, best known, and most media savvy opponent she could have faced. On the other, he was, in many quarters, the most fiercely disliked.
Clinton now will have to retool her campaign strategy, which had put a premium on attacking Giuliani for his abrasive personality and what some see as an unsenatorial characteristic - an inability to get along with others.
''She'll have to sell herself on who she is, not on who she isn't,'' Democratic consultant George Arzt said. ''So far, she hasn't done that.''
The state's Republican leaders are scurrying to come up with a new candidate in time for their party convention on May 30. The most likely choice seems to be Rick Lazio, a four-term congressman from Long Island.
Lazio, 43, had threatened to run against Giuliani in a primary last summer - and raised $3.5 million for the contest - until Governor George Pataki persuaded him to move out of Giuliani's way.
Pataki has also been mentioned as a possible replacement and would probably be the strongest candidate; he is the only Republican who leads Clinton in the polls. However, he has insisted in the past few weeks that he has no interest in leaving his job for the Senate.
Surveys show Clinton with a wide lead over Lazio, but pollster John Zogby said yesterday: ''By next week, I think it will be tied. A lot of Rudy's support was in fact more anti-Hillary than pro-Rudy.''
Giuliani leaves the race with a gracefulness that surprised some, given the unpleasant circumstances of his departure.
Three weeks ago, the 55-year-old mayor stunned the city by announcing that he has prostate cancer. A few days later, he stunned everyone again by confirming reports that he has been seeing a woman, not his wife - and, a few days after that announced he would seek a separation from his wife of 16 years.
A few hours after that declaration, his wife, actress and TV anchorwoman Donna Hanover, appeared outside the governor's Gracie Mansion and blamed the decline of their marriage on an affair that she said the mayor had three years ago with another woman, his former press secretary, Cristyne Lategano. Lategano and the mayor have denied that allegation.
Yesterday's newspapers reported that Hanover has retained one of the city's most high-powered law firms to represent her in drawing up a separation agreement from Giuliani. Many observers took this as a signal that Hanover could have more shocks to deliver.
However, Giuliani said yesterday that his decision to leave the race was based entirely on concerns about his health, not about other aspects of his personal life.
''I decided that what I should do is put my health first,'' he told a packed roomful of reporters, aides, and political supporters in City Hall.
''This is not the right time for me to run for office,'' he added.
Giuliani had been saying for weeks that he would decide what kind of treatment to undergo - surgery, chemotherapy, or radiation pellets - and then determine whether he would have the stamina to go ahead with a Senate campaign.
Yesterday, he said he still had not decided on the treatment but had concluded he could not run an effective campaign, no matter what his choice.
''If I ran, I don't think that I'd concentrate the way I should,'' he said. He also realized he could not predict how he would feel in August or September, when the political race heats up. ''Nobody can tell you on a percentage basis what the side effects are going to be,'' he said.
Giuliani seemed shaken when he started to make his announcement but grew more comfortable, even buoyant, as the half-hour news conference continued.
''Politics is not as important as I thought it was,'' he said. ''I've made a lot of decisions the last 10 years around politics. From now on, I'm going to make them around other things.''
He even called the decision to withdraw ''probably the most useful thing that happened to me, to get me reoriented to what's important in life - I think something good's going to come out of this.''
Then he started talking in a way that nobody has heard, at least publicly, for years.
He noted that leaving the Senate race gives him an additional 18 months to be mayor - his term runs out at the end of 2001 - and that he realizes certain people feel they have been left out of the city's good times.
''I'm going to devote the extra time I've been given,'' he said, ''to overcome some of the barriers that maybe I've placed.'' The remark was clearly a reference to the deep distrust and alienation that many black and Hispanic New Yorkers feel toward the mayor, especially since the police shootings of black immigrants Amadou Diallo and Patrick Dorismond.
It was also rare for Giuliani to admit that he might be responsible for the divide.
The mayor had expressed nearly identical sentiments in his victory speech when he was reelected to a second term in November 1997. However, yesterday, he explicitly recalled that speech and said he regretted that he had not followed through.
''There may be changes I have to make,'' he said. ''I want my time as mayor to count for everybody.''
Thursday night, in a nationally televised town hall meeting, Giuliani had made similar overtures. For the first time, he said he had ''made a mistake'' when he publicly attacked the reputation of Dorismond, a private security guard who was killed by police in a botched drug sting.
''I should have also conveyed the human feeling that I had - of compassion and loss for a mother,'' he said.
The comment led NBC television correspondent Andrea Mitchell, who interviewed him at the meeting Thursday night, to speculate that there might be a ''new Giuliani'' emerging after being confronted with the cancer diagnosis. He laughed off the phrase, and yesterday called it ''silly.''
But, he added at the news conference: ''Maybe it's something when you confront your limits, your mortality. You realize you're not Superman, you're just a human being.''
Giuliani said he had been leaning against running Thursday, but then leaned the other way during that night's well-received town hall meeting.
''I thought, `Gee, I don't know how I can walk away from this - this is so exhilarating,''' he recalled. ''Then I got home, thought about it some more, talked with people some more, couldn't get to sleep till the early hours of the morning.''
But when he woke up, he said, ''I thought, `There are more important things in life.'''
Giuliani leaves the race with $9 million remaining in his campaign war chest. Federal laws prohibit him from turning it over to another candidate, but he could give it to the Republican Party, which could then distribute it. He said yesterday he had not decided what to do with the money, but he said he would do all he can to help his replacement in the race.
