By Doina Chiacu

WASHINGTON (Reuters) - Republican presidential candidate Donald Trump increased his attacks on a former beauty queen with a vague and unsubstantiated allegation about a sex tape in predawn Twitter posts on Friday, and Democratic rival Hillary Clinton denounced him as "unhinged."

Trump's refusal to drop his invective against Alicia Machado, the Miss Universe from Venezuela whom he criticized for gaining weight after she won the crown in 1996, threatened to damage his already weak standing among women and Hispanics.

With less than six weeks to go until the Nov. 8 election, Trump made reference - without giving evidence - to a sex tape involving Machado, who had publicly denounced him all week as a humiliating bully. His attacks provided critics with new fodder to question his temperament for the White House.

"Did Crooked Hillary help disgusting (check out sex tape and past) Alicia M become a U.S. citizen so she could use her in the debate?" Trump said in his Twitter messages in the early hours of Friday. He did not elaborate on his allegations beyond saying that the Clinton campaign was unaware of the beauty queen's past and had been "duped" by her.

At a campaign rally in Coral Springs, Florida, Clinton said the episode was evidence that "a man who can be provoked by a tweet should not have the nuclear codes."

“Who gets up at 3 a.m. in the morning to engage in a Twitter attack against a former Miss Universe? I mean he hurled as many insults as he could. Really, why does he do things like that?

"His latest Twitter meltdown is unhinged, even for him. It proves again he is temperamentally unfit to be President of the United States," she said.

Later on Friday, BuzzFeed said Trump made an appearance in a Playboy softcore pornographic movie from 2000 that it said it had obtained from an online adult video store in New York state.

"Trump’s role in the porn is relatively benign and centers around him breaking a bottle of champagne on a Playboy-branded limo while several of the playmates are visiting New York City," the online media outlet said.

"There's been a lot of talk about sex tapes today and in a strange turn of events only one adult film has emerged today and its star is Donald Trump," Clinton spokesman Nick Merrill told reporters after a campaign event in Florida.

Reuters could not confirm the BuzzFeed report. The Trump campaign did not respond to a Reuters request for comment.

Merrill earlier said Clinton called Machado on Friday to thank her for what he said was the courage she has shown.

Politico reported that Machado has starred in racy reality TV programs and posed naked for Playboy's Mexican version, but said media outlets have found no evidence that she has starred in pornographic films.

Machado, now a U.S. citizen, dismissed the fresh attacks with a message on Instagram, calling them "cheap lies" from a man intent on defaming her.

"By way of his hate campaign, the Republican candidate insists on discrediting and demoralizing a woman, which is clearly one of his most frightening characteristics," she wrote in her post in Spanish, next to a photo of herself draped in an American flag.

AUDIO ISSUE

Clinton raised Trump's treatment of Machado during their first presidential debate on Monday as an example of how he views women. Clinton said Trump, the former owner of the Miss Universe pageants, had called Machado "Miss Piggy" and also "Miss Housekeeping" because she was a Latina.

Trump attacked Machado the following day in a television interview as he sought to rebound from a debate that Clinton was widely viewed as having won. He also promised to hit Clinton harder in their next debate, on Oct. 9, suggesting he might attack Clinton on the infidelities of her husband, former President Bill Clinton.

Speaking to Fox News on Tuesday, Trump said Machado had gained a "massive amount of weight" after her pageant win and that it was a "real problem."

Critics said his offensive this week raised questions about Trump's character. The 70-year-old former reality TV star has never run for office before and his habit of making off-the-cuff insults has alarmed many in the Republican Party establishment.

In taking the bait Clinton dangled on Monday, Trump echoed his August entanglement in a days-long public dispute with the parents of a Muslim Army captain killed in Iraq. That incident caused anguish among many Republican leaders concerned that he had nothing to gain by attacking a grieving family.

Trump's remarks on Friday could hurt him further with women and Hispanic voters. Clinton, 68, a former U.S. senator and secretary of state, is the first woman to win the presidential nomination of a major U.S. political party and has led Trump in opinion polls.

The latest Reuters/Ipsos national tracking poll, released on Friday, showed Clinton leading by 43 percent to Trump's 38 percent among likely voters.

Clinton mocked Trump this week after he complained that he had a faulty microphone during Monday's debate.

The Commission on Presidential Debates said on Friday that, "Regarding the first debate, there were issues regarding Donald Trump's audio that affected the sound level in the debate hall.”

The sound was not affected for the record-setting audience of 84 million people who tuned into the 90-minute exchange.

At a rally in Novi, Michigan, Trump wondered aloud whether the microphone problem was deliberate.

"It's difficult, and when you have a situation like that and you know it's bad and you think that 100 million people are watching, what do you do, stop the show? I wonder why it was bad," he said.

(Additional reporting by Amanda Becker in Florida, Steve Holland in Michigan, Alistair Bell in Washington; Editing by Frances Kerry, Toni Reinhold, Grant McCool, Christian Schmollinger)