WASHINGTON — President Trump announced Monday that Herman Cain, one of his two embattled picks for the Federal Reserve Board, had withdrawn his name from consideration, even as his second candidate came under new scrutiny over his attitudes toward women.
Mr. Cain, a former pizza chain executive, made his decision as he battled old accusations of sexual harassment that had halted his 2012 presidential campaign.
His withdrawal bows to political reality in a moment when Mr. Trump has faced mounting criticism for tapping loyalists to join the historically independent Fed. And it moved a spotlight to the other man Mr. Trump has said he wants to put on the Fed, his economic adviser Stephen Moore, who faced new objections on Monday because of a series of magazine columns that denigrated women, including his wife at the time.
Mr. Moore has called the writings jokes, but the criticism suggests that questions of harassment and sexism could prove more consequential for Mr. Trump’s nominees than interest rates and other policy issues. In his columns, published in the early 2000s by the conservative magazine National Review, some of which were first reported by CNN, he complained that women are “sooo malleable” because his wife at the time voted for a Democrat, based on a campaign commercial.
In other pieces, Mr. Moore said that female tennis players “want equal pay for inferior work” and called it a “travesty” that women wanted to play pickup basketball with men. He called for women to be banned from the N.C.A.A. men’s basketball tournament, unless they were as attractive as the CBS sports journalist Bonnie Bernstein, who, he wrote, “should wear a halter top.”
“Here’s the rule change I propose,” Mr. Moore wrote in 2002. “No more women refs, no women announcers, no women beer vendors, no women anything. There is, of course, an exception to this rule. Women are permitted to participate, if and only if, they look like Bonnie Bernstein. The fact that Bonnie knows nothing about basketball is entirely irrelevant.”
He lamented: “Is there no area in life where men can take vacation from women? What’s next? Women invited to bachelor parties?”
Ms. Bernstein replied on Twitter: “You want halter tops? Hit the club scene. You want hoops knowledge? Try actually listening.”
Mr. Moore, who has not been formally nominated for the Fed board, did not respond to a message seeking comment on the writings on Monday. Earlier in the day, he said in a text message that Mr. Trump would follow through on his nomination “when I get all the paperwork and financial disclosure done.”
Critics previously questioned Mr. Cain’s and Mr. Moore’s shifting views on interest rates, which both men said should be higher under President Barack Obama, when the nation was struggling to recover from the 2008 financial crisis, but now say should stay low under Mr. Trump, when the economy is growing. Both men have previously voiced support of a return to a gold standard, which the United States abandoned decades ago and few economists now support.
Congressional Republicans say those views are less likely to impede Mr. Moore’s confirmation prospects than concerns over his personal life and past statements.
White House officials have insisted in recent weeks that Mr. Moore’s nomination was on track, despite controversies over a $75,000 tax lienfiled against him by the Internal Revenue Service and a judge finding him in contempt of court several years ago for failing to pay more than $300,000 in past-due child support and alimony.
They had been less certain about Mr. Cain, whose selection stoked bipartisan concern over his qualifications for the post and allegations of sexual harassment. At least four Republican senators had said they would oppose his confirmation, if Mr. Trump were to formally nominate him — effectively killing Mr. Cain’s chances in the Senate, where Republicans have 53 seats.
Mr. Cain said Monday afternoon on The Western Journal, a conservative website, that he had decided to withdraw after prayerful consideration, and after questioning whether a Fed seat was worth giving up his online commentary platform and various “business interests,” including paid speeches.
“Without getting too specific about how big a pay cut this would be,” Mr. Cain wrote, “let’s just say I’m pretty confident that if your boss told you to take a similar pay cut, you’d tell him where to go.”
The decision was an abrupt departure from last week, when Mr. Cain vowed to stay in the running, telling The Wall Street Journal he was “very committed” to being nominated. In an op-ed column in that newspaper, Mr. Cain criticized what he called “the professor standard” for Fed nominees under presidents dating to Bill Clinton in the 1990s, which he said had caused the central bank to lose sight of the importance of keeping the dollar strong and stable to support economic growth.
In his column on Monday, Mr. Cain said he had begun to question whether joining the Fed would be, in effect, a step down in influence from his perch writing conservative commentary. “I also started wondering if I’d be giving up too much influence to get a little bit of policy impact,” he wrote.
The president said Mr. Cain had asked him not to nominate him for the seat.
“I will respect his wishes,” Mr. Trump said on Twitter, calling Mr. Cain “a great American who truly loves our country.”
With the attention shifting to Mr. Moore on Monday, Democrats and women’s groups called his comments sexist and disqualifying.
“The report about Stephen Moore making sexist comments about women in sports is disturbing,” said Representative Carolyn B. Maloney of New York, the vice chairwoman of the Joint Economic Committee and a critic of Mr. Moore’s nomination, “and if true would be another reason why he shouldn’t be allowed on the Federal Reserve Board.”
It is unclear whether he, too, might face bipartisan opposition. Some Republicans said privately earlier this month that Mr. Cain’s struggles could help Mr. Moore, because Republican senators would be unlikely to vote against both of Mr. Trump’s nominees. They were more divided on Monday, saying Mr. Cain’s departure could open Mr. Moore to additional scrutiny and attacks.
A senior Republican aide on Capitol Hill said conservatives would be watching how Mr. Moore’s writings about women sat with Senators Lisa Murkowski of Alaska and Susan Collins of Maine, Republicans who are considered swing votes for his nomination. The aide said Mr. Moore’s chances could also depend on whether his ex-wife, Allison, speaks publicly about their difficult divorce and its aftermath.
Records of that divorce were unsealed this month in a Virginia courthouse, and they include allegations of infidelity and Mr. Moore’s failure to pay court-ordered support.
According to filings, in 2010 Mr. Moore started a sexual relationship with a woman he met through an online dating service. His wife found bills that showed Mr. Moore pumping gas in the morning near the home of the other woman and buying an airplane ticket in her name. At their son’s graduation ceremony, Mr. Moore said to his children, in earshot of Ms. Moore, “I have two women, and what’s really bad is when they fight over you.”
Before the divorce, Mr. Moore frequently teased his ex-wife in his National Review columns. In 2001, he wrote that “she’s been acting as if it’s her patriotic duty to single-handedly revive the American economy with her frenetic pace of consumer spending.” In 2003, he wrote that “Allison consumes but she still doesn’t produce.” In 2004, he wrote, “Here’s the best news of all: For once, Allison isn’t pregnant.”
Others columns criticized the notion of a “pay gap” between male and female athletes.
“Women tennis pros don’t really want equal pay for equal work. They want equal pay for inferior work,” Mr. Moore wrote in 2000. “If there is an injustice in tennis, it’s that women like Martina Hingis and Monica Seles make millions of dollars a year, even though there are hundreds of men at the collegiate level (assuming their schools haven’t dropped the sport) who could beat them handily.”
Kitty Bennett contributed research.