Donald Trump was emphatic in the second presidential debate: Yes, he had boasted about kissing women without permission and grabbing their genitals. But he had never actually done those things, he said.

"No," he declared under questioning Sunday evening, "I have not."

At that moment, sitting at home in Manhattan, Jessica Leeds, 74, felt he was lying to her face. "I wanted to punch the screen," she said in an interview in her apartment.

More than three decades ago, when she was a traveling businesswoman at a paper company, Leeds said, she sat beside Trump in the first-class cabin of a flight to New York. They had never met.

About 45 minutes after takeoff, she recalled, Trump lifted the armrest and began to touch her.

According to Leeds, Trump grabbed her breasts and tried to put his hand up her skirt.

"He was like an octopus," she said. "His hands were everywhere."

She fled to the back of the plane.

"It was an assault," she said.

Leeds has told the story to at least four people close to her, who also spoke with The New York Times.

Jessica Leeds, a businesswoman at a paper company who was sitting next to Donald Trump on a flight to New York in the early 1980s, speaks at her home in New York. Leeds, who had never met Trump, said that during the flight, he lifted the armrest and began to touch her. (George Etheredge/The New York Times)

Trump's claim that his crude words had never turned into actions was similarly infuriating to a woman watching on Sunday night in Ohio: Rachel Crooks.

Crooks was a 22-year-old receptionist at Bayrock Group, a real estate investment and development company in Trump Tower in Manhattan, when she encountered Trump outside an elevator in the building one morning in 2005.

Aware that her company did business with Trump, she turned and introduced herself. They shook hands, but Mr. Trump would not let go, she said. Instead, he began kissing her cheeks. Then, she said, he "kissed me directly on the mouth."

It didn't feel like an accident, she said. It felt like a violation.

"It was so inappropriate," Crooks recalled. "I was so upset that he thought I was so insignificant that he could do that."

Shaken, Crooks returned to her desk and immediately called her sister, Brianne Webb, and told her what had happened.

"She was very worked up about it," said Webb, who recalled pressing her sister for details. "Being from a town of 1,600 people, being naïve, I was like, 'Are you sure he didn't just miss trying to kiss you on the cheek?' She said, 'No, he kissed me on the mouth.' I was like, 'That is not normal.'"

In the days since Trump's campaign was jolted by a 2005 recording that caught him bragging about pushing himself on women, he has insisted, as have his aides, that it was simply macho bluster. "It's just words," he has said repeatedly.

And his hope for salvaging his candidacy rests heavily on whether voters believe that claim.

They should not, say Leeds and Crooks, whose stories have never been made public.

And their accounts echo those of other women who have previously come forward, like Temple Taggart, a former Miss Utah, who said that Trump kissed her on the mouth more than once when she was a 21-year-old beauty pageant contestant.

Trump's campaign released a statement Wednesday evening in response to the claims, with spokesman Jason Miller calling The Times' reporting "fiction."

"For The New York Times to launch a completely false, coordinated character assassination against Mr. Trump on a topic like this is dangerous," Miller said. "To reach back decades in an attempt to smear Mr. Trump trivializes sexual assault, and it sets a new low for where the media is willing to go in its efforts to determine this election."

Trump, notably, held a news conference before Sunday's debate with three women who had accused Bill Clinton of sexual assault and harassment in the 1970s and 1990s, and a woman whose alleged rapist Hillary Clinton defended in 1975.

During a phone interview Tuesday night, a highly agitated Trump denied every one of Crooks' and Leeds' claims.

"None of this ever took place," said Trump, who began shouting at the reporter who was questioning him.

He said that The Times was making up the allegations to hurt him and that he would sue the news organization if it reported them.

"You are a disgusting human being," he told the reporter as she questioned him about the women's claims.

Asked Tuesday whether he had ever done any of the kissing or groping that he had described on the recording, Trump was once again insistent: "I don't do it. I don't do it. It was locker-room talk."

Late Wednesday night the Trump campaign released a letter to reporters that they say was sent to Times Executive Editor Dean Baquet threatening legal action if the story is not retracted.

"I think it is pretty evident this story falls clearly in the realm of public service journalism, and discussing issues that arose from the tape and his comments since it surfaced," Baquet told CNN's Brian Stelter.

Trump has threatened to file lawsuits against The Times and other media outlets before. Two weeks ago, Trump's lawyer Marc Kasowitz threatened to sue the newspaper for invasion of privacy in reaction to its publishing excerpts from his tax returns. Trump continued to talk about the potential suit at political rallies, but said that he was holding off on filing.

The Times famously won the landmark Supreme Court case New York Times v. Sullivan which established the actual malice standard. The standard must be met before news reports about public officials can be considered defamation or libel.

But for the women who shared their stories with The Times, the recording was more than that: As upsetting as it was, it offered them a kind of affirmation, they said.

That was the case for Taggart. Trump's description of how he kisses beautiful women without invitation described precisely what he did to her, she said.

"I just start kissing them," Trump said on the tape. "It's like a magnet. Just kiss. I don't even wait."

Several other women have accused Trump of sexual assault since The Times' report was published.

Wednesday evening, The Palm Beach Post reported that another woman, 36-year-old Mindy McGillivray, said Trump groped her 13 years ago at his Mar-A-Lago estate in Florida.

McGillivray said she never reported it to police, but photographer Ken Davidoff, who was with her that day, said he vividly remembered her telling him moments after the incident.

Trump's press secretary, Hope Hicks, said there was no truth to McGillivray's claim.

People magazine writer Natasha Stoynoff published her account of being physically attacked by Trump at his Mar-a-Largo estate in December 2005. Stoynoff writes that she was on assignment to interview Trump and his wife Melania around the same time Trump's conversation with Billy Bush was caught on tape.

Stoynoff writes that Trump told her there was a "tremendous" room that she had to see. When they walked into the room alone, Trump shut the door.

"I turn around and within seconds, he was pushing me against the wall, and forcing his tongue down my throat," she writes.

After Stoynoff returned to New York she told a colleague what had happened. The colleague suggested they tell the Managing Editor. Stoynoff requested to be taken off the magazine's beat covering the Trumps and never interviewed him again.

A spokesperson for Trump told People, "This never happened. There is no merit or veracity to this fictional story. Why wasn't this reported at the time? Mr. Trump was the biggest star on television and surely this would have been a far bigger scoop for People magazine. She alleges this took place in a public space with people around. This is nothing by politically motivated fictional pile-on."

Slate has complied a list of the women who have accused Trump.

Crooks and Leeds never reported their accounts to authorities, but they both shared what happened to them with friends and family. Crooks did so immediately afterward; Leeds described the events to those close to her more recently, as Trump became more visible politically and ran for president.

Jessica Leeds in 1978. (Jessica Leeds)

Leeds was 38 at the time and living in Connecticut. She had been seated in coach. But a flight attendant invited her to take an empty seat in first class, she said. That seat was beside Trump, who did not yet own a fleet of private aircraft, records show. He introduced himself and shook her hand. They exchanged pleasantries, and Trump asked her whether she was married. She was divorced, and told him so.

Later, after their dinner trays were cleared, she said, Trump raised the armrest, moved toward her and began to grope her. Leeds said she recoiled. She quickly left the first-class cabin and returned to coach, she said.

"I was angry and shook up," she recalled, as she sat on a couch in her New York City apartment on Tuesday.

She did not complain to the airline staff at the time, Leeds said, because such unwanted advances from men occurred throughout her time in business in the 1970s and early 1980s.

"We accepted it for years," she said of the conduct. "We were taught it was our fault."

She recalled bumping into Trump at a charity event in New York about two years later, and said he seemed to recall her, insulting her with a crude remark.

She had largely put the encounter on the plane out of her mind until last year, when Trump's presidential campaign became more serious. Since then, she has told a widening circle of people, including her son, a nephew and two friends, all of whom were contacted by The Times.

They said they were sickened by what they heard.

"It made me shake," said Linda Ross, a neighbor and friend who spoke with Leeds about the interaction about six months ago. Like several of Leeds' friends, Ross encouraged her to tell the media. Leeds had resisted until Sunday's debate, which she watched with Ross.

When Trump denied having ever sexually assaulted women, in response to a question from CNN's Anderson Cooper, Ross said she immediately looked at Leeds in disbelief. "Now we know he lied straight up," Ross recalled saying.

In the days after the debate, Leeds recounted her experience in an email to The Times and a series of interviews.

"His behavior is deep seated in his character," Leeds wrote.

"To those who would vote for him," she added, "I would wish for them to reflect on this."

For Crooks, the encounter with Trump was further complicated by the fact that she worked in his building and risked running into him again.

A few hours after Trump kissed her, Crooks returned to her apartment in Brooklyn and broke down to her boyfriend at the time, Clint Hackenburg.

"I asked, 'How was your day?'" Hackenburg said. "She paused for a second, and then started hysterically crying."

After Crooks described her experience with Trump, she and Hackenburg discussed what to do.

"I think that what was more upsetting than him kissing her was that she felt like she couldn't do anything to him because of his position," he said. "She was 22. She was a secretary. It was her first job out of college. I remember her saying, 'I can't do anything to this guy, because he's Donald Trump.'"

Days later, Crooks said, Trump, who had recently married Melania Trump, came into the Bayrock office and requested her phone number. When she asked why he needed it, Trump told her he intended to pass it along to his modeling agency. Crooks was skeptical, but relented because of Trump's influence over her company. She never heard from the modeling agency.

During the rest of her year working at Bayrock, she made a point of ducking out of sight every time Trump came into view. When Bayrock employees were invited to the Trump Organization Christmas party, she declined, wanting to avoid any other encounters with him.

But the episode stuck with her even after she returned to Ohio, where she now works for a university. When she read a Times article in May about the Republican nominee's treatment of women, she was struck by Taggart's recollection of being kissed on the mouth by Mr. Trump.

"I was upset that it had happened to other people, but also took some comfort in knowing I wasn't the only one he had done it to," said Crooks, who reached out to The Times to share her story.

Both Leeds and Crooks say they support Hillary Clinton's campaign for president, and Crooks has made contributions of less than $200 to Barack Obama and Clinton.

Crooks was initially reluctant to go public with her story, but felt compelled to talk about her experience.

"People should know," she said of Trump, "this behavior is pervasive and it is real."

By Megan Twohey and Michael Barbaro, The New York Times

Posted by breaking news producer Tom Steele, breaking news reporter Hannah Wise contributed.