New York Gov. David Paterson, defying calls from even fellow Democrats to drop out of the race for a full term, said Tuesday that he would leave only if the voters turned him out through the ballot box, or “in a box.”

Paterson spoke to reporters after several days of rumors sweeping the state Capitol about carousing in the governor’s mansion, all of which Paterson strongly denied.

A few months after Paterson took over from his predecessor, who resigned in a prostitution scandal, his popularity plummeted and many Democrats voiced their preference that Attorney General Andrew Cuomo run for governor when Paterson’s term is up.

That infighting and the recent rumormongering have further fractured state Democrats and added a decidedly weird edge to the national party’s struggle to maintain ground it gained in the last election.

Facing challenges from coast to coast amid voter frustration with incumbents of both parties, Democrats in particular are girding for losses that could see states’ chief executives go into Republican hands. New York, a traditionally Democratic-leaning state, would be a devastating blow to a party that just two years ago saw a landslide amid the election of President Barack Obama.

Paterson appeared to take heart from an interview earlier in the day with The New York Times, which had been widely anticipated to be preparing a story dealing with his personal conduct. He said that in the interview he was not asked about drug use in the governor’s mansion or partying with women.

“The only way I’m not going to be governor next year is at the ballot box, and the only way that I will be leaving the office before is in a box,” Paterson said during a news conference.

Paterson had decried the allegations Monday in an Associated Press interview.

He has been trying to end one of the weirdest travails yet in a weird place, a political “Twilight Zone” he often refers to as Planet Albany. This time, media coverage alternately derided as a feeding frenzy and a circus, involved one of the world’s most influential newspapers and became a scandal about a scandal that was yet to be written and which, according to Paterson, won’t be.

“Obviously we are not responsible for what other news organizations are reporting,” said Times spokeswoman Diane C. McNulty. “It’s not coming from The Times.”

Paterson attributed the rumors to news outlets and blogs other than the Times. He said that three sources contacted reporters at the start of Sunday’s Super Bowl to leak word that he was about to resign, which he said he never contemplated.

“It seems to be somewhat orchestrated,” Paterson said Tuesday of the rumors, on whose source he has declined to publicly speculate.

One item by the New York Post on Jan. 30 stated he was caught by state police in a utility closet with a woman other than his wife. The Post has stood by its story. Paterson said a Times reporter who interviewed him Tuesday in the mansion couldn’t even find such a closet.

He said Tuesday that after his interview with the Times, he expects its article to be a profile, not about sexual escapades or drug use.

“No such questions, really, to any of that was asked of me,” he said.

The news conference, Paterson’s first since the rumors started, was ostensibly called to announce plans for combatting a snowstorm. But it was clear to reporters and staffers that Paterson wanted the time to publicly declare victory over the rumors, armed with what he learned from the Times interview hours before.

He said his two children and his wife have been supportive through the week of innuendo, with one consistent message: “Don’t give up, even if you are ridiculed.”

Most of Paterson’s fellow top Democrats were silent as the governor sought to snuff out the rumors. Cuomo refused to comment on the unsubstantiated tales, and his office wouldn’t comment on whether he supports Paterson in his battle.

“We don’t comment on rumors,” Cuomo spokesman Richard Bamberger said. “There are serious problems facing our state and the attorney general is busy doing the job he was elected to do.”

Many Democrats have voiced wishes that Cuomo run for governor instead of Paterson, a former lieutenant governor who took the post in 2008 upon the resignation of Eliot Spitzer, named in a prostitution investigation 23 months ago.

A day after taking office, Paterson told a news conference that he had not been faithful to his wife around 1999 when they informally separated. A week later he told a television interviewer that he had tried cocaine and marijuana when he was in his early 20s — hardly the first few story lines a new governor would seek.

The White House last year, recognizing the challenges of helping an accidental governor keep his office, urged him to withdraw from the race in favor of Cuomo, part of a Democratic dynasty in New York who could defend the office.

A Republican candidate for governor sided with Paterson on Tuesday.

“The Capitol is paralyzed by rumor and innuendo, and somehow we need to get past that and focus on the basic problems that people care about,” Rick Lazio said. “I don’t think anyone trying to get their job done deserves this kind of phantom threat.”

Paterson Chief of Staff Lawrence Schwartz released a letter late Tuesday to the public editor of the Times seeking an inquiry.

“At any point, the Times’ editors could have easily issued a public statement clarifying that the profile neither contained nor supported the salacious stories being sourced to it,” Schwartz wrote. “Common decency, if not journalistic ethics, demanded as much.”

Democratic state leaders wouldn’t comment on Paterson or the rumors as he confronts the Legislature over the state budget, an ethics bill he vetoed and the awarding of a contract for video slot machines at Aqueduct race track.

Senate Conference Leader John Sampson, a Brooklyn Democrat at odds with Paterson in legislative fights, declined to comment. Democratic Sen. Charles Schumer also wouldn’t comment, and Assembly Speaker Sheldon Silver, a Manhattan Democrat, didn’t immediately respond to a request for comment.