The new accusations come as Trump slips further behind Democratic candidate Hillary Clinton in national opinion polls ahead of the November 8 election. A Reuters/Ipsos survey this week showed him lagging Clinton by 8 percentage points among likely voters.
Summer Zervos, who competed on the television show's fifth season in 2006, gave a news conference with celebrity attorney Gloria Allred in Los Angeles, saying Trump tried to get her to lie down on a bed with him when she met him in 2007 to discuss a possible job.
"He then asked me to sit next to him. I complied. He then grabbed my shoulder and began kissing me again very aggressively and placed his hand on my breast," said Zervos.
Separately, the Washington Post published an interview with a woman who said Trump put his hand up her skirt in a crowded New York nightclub in the early 1990s in an unwanted advance, when she had never even met him.
"He did touch my vagina through my underwear, absolutely," Kristin Anderson said in a video interview on the newspaper's website. "It wasn't a sexual come-on. I don't know why he did it. It was like just to prove that he could do it," she told the paper. Anderson could not immediately be reached for comment.
The Trump campaign did not immediately respond to requests for comment on the new allegations. But at a campaign rally on Friday afternoon, Trump angrily denounced the allegations that have been made about him by a series of women in recent days, calling the women "sick" and saying that all the accusations were fabricated.
"I don't know who these people are. I look on television, I think it's a disgusting thing and it's being pushed, they have no witnesses, there's nobody around," Trump said at the rally in Greensboro, N.C..
"Some are doing it for probably a little fame, they get some free fame. It's a total set-up. Now suddenly after many, many years, phony accusers come out less than a month before one of the most important elections in the history of our country," he said.
Trump's White House campaign has been scrambling to recover from the release a week ago of a 2005 video in which he bragged about groping women and making unwanted sexual advances. While Trump said the video was just talk and he had never behaved in this way, multiple women subsequently went public with allegations of sexual misconduct against the New York real estate magnate going back three decades.
Support from Pence
Earlier on Friday, Republican vice presidential candidate Mike Pence defended Trump. "Stay tuned. I know there's more information that's going to be coming out that will back his claim that this is all categorically false," Pence told CBS show "This Morning."
Pence did not give any details about what information would be forthcoming. Trump also said on Thursday that he would make public information showing the allegations against him were false, without giving details.
In denying the allegations, Trump has said The New York Times, which published two women's claims, and other media, along with Clinton, are engaged in a vicious campaign to stop him from winning the election.
The Times reported on Wednesday that two women said they had endured unwanted groping or kisses from the former TV personality. Several other women made allegations of sexual aggression by Trump in various media outlets following that report.
Reuters could not independently verify the incidents. The Times said on Thursday it stood by its story and rejected charges the article was libelous after a lawyer for Trump threatened legal action and demanded a retraction.
Trump on Friday mocked one of the women cited in the Times article, Jessica Leeds. "Yeah, I'm going to go after. Believe me, she would not be my first choice, that I can tell you. You don't know. That would not be my first choice." Leeds, who is now 74, alleged that Trump groped her on a flight to New York, in or around 1980.
He called Natasha Stoynoff, a reporter who wrote in People magazine that Trump kissed her and pinned her against a wall, a "liar" and told the rally to "check out her Facebook page, you'll understand."
Disputes with Mexico
Trump also accused Mexican billionaire Carlos Slim - the top shareholder in The New York Times Company - of helping to generate the reports of sexual misconduct.
He said Slim, as a donor to the Clinton Foundation charity who also holds a 17.35 percent stake in the Times, has an interest in helping her White House campaign.
"He's given many millions of dollars to the Clintons and their initiatives," Trump said. "Reporters at the New York Times, they're not journalists, they're corporate lobbyists for Carlos Slim and for Hillary Clinton," he said.
Arturo Elias, Slim's spokesman and son-in-law, said Slim had "absolutely no contact" with the newspaper's reporters or editors on their Trump campaign coverage and "zero" contact with the paper's news operations.
New York Times publisher Arthur Sulzberger Jr. said in a statement, "Carlos Slim is an excellent shareholder who fully respects boundaries regarding the independence of our journalism. He has never sought to influence what we report."
Trump's allegation about Slim was the latest chapter in a running series of skirmishes he has had with Mexico and Mexicans.
Trump kicked off his campaign last year accusing Mexico of sending rapists and drug dealers to the United States and promised to build a wall along the southern U.S. border that he said he would make Mexico pay for.
He also pledged to tear up or revise the North American Free Trade Agreement. The Mexican peso slid to record lows in September when Trump was close to Clinton in opinion polls, but the currency has since climbed back.
