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The fallout from the story mounted during the day. Investors fled shares of Wynn Resorts, Mr. Wynn’s casino company, driving the stock price down 10 percent.

Gambling officials in Massachusetts, where Mr. Wynn’s company plans to open a $2.4 billion casino resort near Boston next year, said they had opened a review into the “troubling allegations” of Mr. Wynn’s behavior “to determine the appropriate next steps.”

The Wynn Resorts board met on Friday to form a committee of independent directors to investigate the allegations, saying in a statement that it is “deeply committed to ensuring the safety and well-being of all of the company’s employees and to operating with the highest ethical standards.”

The allegations could also have political impact as well. Mr. Wynn was named chairman of the Republican National Committee’s finance committee shortly after the election of President Trump in November 2016. Mr. Trump has described Mr. Wynn as a friend.

Mr. Wynn and his companies have donated more than $5.2 million over the years to a mix of Republican and Democratic candidates and committees.

A spokesman for the R.N.C. did not respond to questions about whether Mr. Wynn would remain as the party’s finance chairman.

Michael Weaver, a spokesman for Mr. Wynn’s company, declined to comment when asked whether Mr. Wynn intended to step down from his R.N.C. post, and also declined to specify the last time Mr. Wynn had spoken to Mr. Trump. “In the past, Mr. Wynn has not disclosed publicly when he speaks to the president,” Mr. Weaver wrote in an email.

The allegations against Mr. Wynn are similar to the long history of sexual assault and misconduct documented by The New York Times in October against the movie mogul Harvey Weinstein. The report on Mr. Weinstein set off a wave of news reports about allegations of sexual misconduct and harassment against powerful men in Hollywood, the news media, politics, the arts, restaurants and other industries.

The onslaught of news reports about sexually aggressive men has been fueled, in part, by women coming forward to share their stories of sexual harassment under the banner of #MeToo.

Wynn Resort’s Stock Price

Mr. Wynn, who turns 76 on Saturday, is one of the most powerful figures in the casino industry. Like Mr. Trump, he is known for splashing his name on his casinos and resorts, and his signature is the company’s logo.

His ornate casinos, which included the Bellagio, the Mirage, Treasure Island and Wynn, helped change the image of the Las Vegas Strip into one encapsulating glamour, fancy restaurants and exotic attractions like the lion-taming duo of Siegfried & Roy at the Mirage. The Bellagio, a huge hotel and casino on the strip, features an array of dancing water fountains that routinely fascinate tourists. Mr. Wynn eventually sold the Bellagio, along with the Mirage and Treasure Island.

Mr. Wynn made more than $28 million in total compensation from Wynn Resorts for 2016.

“The thing about Steve Wynn is this: He is the biggest name in the history of Nevada business,” said Jon Ralston, the editor of The Nevada Independent, who has reported on the state’s gaming industry for decades.

“People throw around the word ‘visionary’ all the time,” he said. “This guy really was a visionary.”

The allegations against Mr. Wynn are notable because he is one of the most prominent executives of a large public company to be hit with multiple claims of sexual misconduct. The claims could tarnish his company’s brand because his name is so closely identified with it. And given that casinos are a state-regulated industry, the allegations could have an impact on the company’s management of the casino resorts it operates and other projects under construction.

His planned casino near Boston came under scrutiny on Friday when the Massachusetts Gaming Commission said, “The suitability and integrity of our gaming licensees is of the utmost importance, and ensuring that suitability is an active and ongoing process.”

Democrats sought to capitalize on the revelations.

They pointed out that Mr. Wynn and the R.N.C.’s chairwoman, Ronna McDaniel, hosted a fund-raiser at Mr. Trump’s Mar-a-Lago club in Palm Beach, Fla., just last week to celebrate the one-year anniversary of his inauguration. Democrats noted that in the wake of The Times’s exposé on Mr. Weinstein’s decades-long pattern of sexual misconduct, Republicans had blasted Democrats for accepting donations from the Hollywood producer.

Representative Jacky Rosen of Nevada, a Democrat who is running for Senate, called on Dean Heller, a Republican senator from the state, to disavow support he had received from Mr. Wynn. She called the allegations “horrifying and disturbing.”

Mr. Wynn’s selection as the R.N.C.’s finance chairman under Mr. Trump last year struck some in G.O.P. finance circles as odd. Mr. Wynn had initially supported Mr. Trump’s rival, Senator Marco Rubio of Florida, for the party’s nomination.

A registered Democrat for decades, Mr. Wynn had long dabbled in politics, but had focused mostly on Nevada. He was seen a business-minded centrist who cultivated politicians from both parties who could help his business interests.

Mr. Wynn pivoted sharply to the right in response to President Barack Obama’s pushes to pass an economic stimulus bill and overhaul the nation’s health care system.

Mr. Wynn and the company, in statements, both sought to cast blame for the allegations on Mr. Wynn’s former wife, Elaine Wynn, saying she has been making allegations of sexual misconduct in court proceedings to further her financial interests in litigation against the casino mogul.

An allegation of misconduct by Mr. Wynn first appeared in a court filing by Ms. Wynn in state court in Nevada. In that filing, Ms. Wynn said she had learned that her former husband made a multimillion-dollar payment in 2005 “after being threatened with allegations of serious misconduct” against a Wynn employee on a company property.

The Journal story said the 2005 settlement involved a payment of $7.5 million to a manicurist who worked at one of his Las Vegas resorts. The newspaper said Mr. Wynn pressured the woman to take off her clothes and to have sex with him, even though she did not want to.

Mark E. Ferrario, one of Ms. Wynn’s lawyers, did not respond to requests for comment.

In an earlier statement, Wynn Resorts said: “It is clear that Mr. Wynn’s ex-wife has sought to use a negative public relations campaign to achieve what she has been unable to do in the courtroom: tarnish the reputation of Mr. Wynn in an attempt to pressure a revised divorce settlement from him.”

As for Wynn Resorts, the company is continuing to build and grow in Las Vegas.

It reached an agreement last month to buy 38 acres of land on the Las Vegas Strip directly across from Wynn Las Vegas for $336 million.