“Steve won the battle of ideas including Tax Cuts and deregulation which have produced non-inflationary prosperity for all Americans,” Trump tweeted. “I’ve asked Steve to work with me toward future economic growth in our Country.”

In a letter informing Trump of his decision to withdraw, Moore praised the president’s economic policies but said the scrutiny of his past remarks had become too much to bear.

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“Trumponomics has been VINDICATED,” Moore wrote. “Your confidence in me makes what I am about to say much harder. I am respectfully asking that you withdraw my name from consideration. The unrelenting attacks on my character have become untenable for me and my family and 3 more months of this would be too hard on us.”

A growing number of Republican senators said they had serious problems with Moore over his questionable writings, and the White House, which said Monday that it was reviewing those writings, never formally submitted his nomination.

Among the Republicans most critical of Moore was Sen. Joni Ernst (Iowa), who had become increasingly incensed about Moore’s nomination throughout this week and told The Washington Post on Wednesday, “I sure would like to see him just withdraw.”

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“Very, very thankful that he decided not to pursue it,” Ernst said shortly after Trump’s announcement on Thursday. “Bottom line, they need to vet all of that, even before they forward a name or float a name out there. Let’s please do some research.”

Moore’s decision comes after Herman Cain, another Trump choice for the Fed Board, stepped aside as it was clear that he similarly lacked support in the Senate, where Republicans control 53 votes. The 2012 presidential candidate had faced multiple accusations of sexual misconduct and harassment, which he denied.

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Despite the GOP advantage in the Senate, Moore and Cain are far from the only Trump nominees Republicans have tanked because of their writings or questions about their qualifications. At least five judicial candidates failed to advance after GOP senators raised objections, and Cabinet nominees such as Ronny L. Jackson for Veterans Affairs and Andrew Puzder for the Labor Department also stepped aside after it was clear there was no support for them in the GOP-controlled Senate.

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Senate Majority Leader Mitch McConnell (R-Ky.) regularly advises GOP senators to air their complaints about nominees directly to the White House, and the Moore episode, in particular, prompted Senate Republicans to be more vocal with their concerns about the administration’s vetting practices.

“Read people’s articles that they write would be a good start,” said Sen. Shelley Moore Capito (R-W.Va.).

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“Vet better,” said Sen. Lindsey O. Graham (R-S.C.), one of the president’s closest allies.

“I can’t tell them what to do,” said Senate Majority Whip John Thune (S.D.), the Senate’s second-ranking Republican. “But . . . we could always do a better job of interacting — us with them, and them with us.”

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Democrats welcomed the news of Moore’s withdrawal.

“The only thing less funny than some of Mr. Moore’s tasteless, offensive, sexist ‘jokes’ was the idea that President Trump would even consider him for a seat on the Federal Reserve,” Senate Minority Leader Charles E. Schumer (D-N.Y.) said in a statement.

On Wednesday afternoon, Moore wrote in a text message to The Post that he was “full speed ahead” despite the mounting GOP pushback in the Senate that made his confirmation all but impossible. Even some White House officials had begun wondering on Wednesday when Moore would pull back from consideration, but White House National Economic Council Director Larry Kudlow had insisted that Moore still had ample support and that the White House would not back down.

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Sen. Mike Lee (R-Utah), who organizes a lunch on Wednesdays for Republican senators, had wanted to invite Moore to speak at this week’s gathering but was advised against doing so by the White House, according to an official familiar with the planning. A spokesman for Lee said the office doesn’t comment on lunch preparations.

Moore visited with Bloomberg News journalists on Thursday morning and insisted he was still seeking confirmation, but several hours later Trump announced Moore’s decision to pull back. It could not be immediately learned what took place between those two events.

Moore marks the fourth consecutive Fed Board nominee or near-nominee to fall short before even receiving a Senate vote, a rare stretch, particularly when the White House and Senate are controlled by the same party. Following the advice of aides, Trump had nominated Marvin Goodfriend and Nellie Liang to join the Fed Board last year, but their nominations languished.

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Amid growing frustration with the Fed late last year, Trump sought to take over the process and appoint people he thought would be more loyal to him and who shared his call to slash interest rates in a way he thought would grow the economy more quickly. He then announced he would tap Cain and Moore to the two Fed Board seats that remained open.

There are seven Fed Board governors, and the central bank votes every six weeks on interest rate policy. In recent decades, White House officials have largely abstained from directly criticizing the Fed’s approach to monetary policy, seeking to wall the central bank off from allegations of political interference. But Trump and his aides abandoned that precedent recently, and Trump has even mulled trying to oust Fed Board Chair Jerome H. Powell, whom he appointed to succeed Janet L. Yellen.

In recent weeks, Moore had been defiant amid revelations about columns in the 2000s in which he made derogatory statements about women, called for then-Georgia Gov. Sonny Perdue (R) to be impeached and made a joking reference to AIDS.

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Last month, in an interview with North Dakota-based radio station WZFG, Moore accused his opponents of “pulling a Kavanaugh against me.”

Moore’s statement was a reference to Supreme Court Justice Brett M. Kavanaugh, who faced allegations amid his confirmation hearings last year of sexual misconduct during his college and high school years — accusations he denied. Conservatives rallied to Kavanaugh’s defense, and he was narrowly confirmed by the Senate.

Moore also came under scrutiny for saying in 2016 that it would be a “betrayal” for Trump to pick former Massachusetts governor Mitt Romney (R) to be secretary of state. Romney now represents Utah in the Senate and expressed some trepidation to reporters this week about Moore’s old writings.

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A 2014 comment by Moore that Cincinnati and Cleveland are “armpits of America” drew a rebuke from Sen. Sherrod Brown (D-Ohio), who wrote a letter to Moore last month calling the remarks “disqualifying” and demanding that he provide a list of other towns that he would describe as “armpits.”

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Ohio is a swing state that was central to Trump’s win in 2016 and will be a key part of his 2020 reelection efforts.

Last month, CNN resurfaced several columns in which Moore decried the “feminization of basketball,” denounced co-ed sports and argued that women should not be allowed to be men’s sports referees — unless they are good-looking.

Moore also wrote that female athletes were seeking “equal pay for inferior work” and lamented, “Is there no area in life where men can take vacation from women?”

Moore told The Post last month that he did not stand by any of the comments and that the column was a “spoof,” although he did not cite a particular column or explain a later piece in which he defended his remarks.

In a recent article, CNBC also unearthed some of Moore’s past writings, including one in 2004 in which he wrote about being told by a doctor that his young son had “low-muscle tone.”

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“He might as well have told us that [the child] has AIDS,” Moore wrote.

Moore also repeatedly made mocking references to his wife at the time, a stay-at-home mother, as a “loss leader” who “doesn’t have a job.”

Stephen and Allison Moore, who have three children together, were married for two decades before divorcing in 2011. Allison Moore began divorce proceedings in 2010, and her divorce complaint said her then-husband had opened a Match.com account and had a mistress.

Stephen Moore was found in contempt of court in 2013 for failing to pay his ex-wife more than $330,000 in alimony and child support, court documents show.

The New York Times found other Moore columns. In one, written in 2000 for the Washington Times, Moore described colleges as “places for rabble-rousing” and “for men to lose their boyhood innocence” and “do stupid things.”

“It’s all a time-tested rite of passage into adulthood,” he wrote. “And the women seemed to survive just fine. If they were so oppressed and offended by drunken, lustful frat boys, why is it that on Friday nights they showed up in droves in tight skirts to the keg parties?”

Moore also said in a 2016 speech that if Trump won the White House, he would “kick a black family out of public housing,” a reference to the Obamas. He expressed regret for the remark in an interview this week with PBS’s “Firing Line with Margaret Hoover.”

Two of Moore’s other past statements seemed problematic.

In a 2003 National Review column titled “Impeach Governor Sonny Perdue,” Moore blasted Georgia’s then-governor — and Trump’s current agriculture secretary — over tax policy.

“Voters thought they were electing a Ronald Reagan, not a Michael Dukakis,” Moore wrote in the piece, describing Perdue and other Georgia Republicans as “fiscal frauds.”

Sen. David Perdue (R-Ga.), Perdue’s cousin, is a member of the Senate Banking Committee, which would have held a hearing on Moore’s nomination as part of the confirmation process.

In an email, Moore told The Post that he and Sonny Perdue had reconciled “many years ago.”

“I had a great meeting with him several months after our policy disagreement and have had a friendship with him ever since,” Moore said.

Moore also said in a 2016 radio interview that a potential nomination of Romney by Trump to be secretary of state “makes me so angry,” according to a CNN report at the time.