Donald Trump tweeted an image that came from a June 15 tweet by @FishBoneHead1, an account with a penchant for memes that mock Muslims, black Democrats and more. Trump later deleted the tweet and uploaded it with a circle instead of a red Star of David. (Twitter screengrab)

Donald Trump struggled Tuesday to move past his latest social-media firestorm for the fourth consecutive day, facing a bipartisan scolding for tweeting a controversial image attacking Hillary Clinton that was widely viewed as anti-Semitic.

House Speaker Paul D. Ryan (R-Wis.) said in a radio interview that anti-Semitic images have “no place in a presidential campaign” and added, “I don’t know what flunky put this up there.” Some leading Jewish Republican donors and activists also voiced concerns about Trump’s habit of posting material that originated in racist, white supremacist corners of the Internet.

Trump’s son-in-law and close campaign confidant Jared Kushner, who is Jewish, also faced blowback. An entertainment writer at the New York Observer posted an open letter to Kushner online urging him to rebuke the tweet. Kushner, who is married to Trump’s daughter Ivanka, is the publisher of the Observer.

Kushner released a statement calling Trump an “incredibly loving and tolerant person who has embraced my family and our Judaism since I began dating my wife." He said that “the suggestion that he may be intolerant is not reflective of the Donald Trump I know.”

Clinton, who condemned the tweet over the weekend, on Tuesday posted a video on Twitter of Trump in a TV interview this year waffling over whether to denounce the support of former Ku Klux Klan leader David Duke and other white supremacists. In interviews before and after that, Trump denounced Duke.

GOP presidential candidate Donald Trump faced a backlash after posting a tweet of Hillary Clinton next to $100 bills and a Star of David-like logo. The Post’s Robert Costa explains why this latest controversy is typical of the way Trump’s campaign operates. (Bastien Inzaurralde/The Washington Post)

For some, Trump’s tweet and the ensuing backlash have highlighted an enduring problem the presumptive GOP nominee has not been able to put to rest: his occasional posting of racially charged messages on social media that could be avoided with more careful research and vetting. For others, the episode has served as a troubling reminder that Trump’s campaign, which has centered on calls to deport immigrants and ban Muslims, has attracted strong support among the white nationalist movement.

“I think that it’s really, really clear — the point is, I think he’s got to clean this up,” Ryan told conservative host Charlie Sykes on WTMJ radio in Milwaukee. “My understanding is this is done by staff, not by he himself.”

The controversy erupted Saturday morning after a tweet from Trump’s account showed an image of Clinton’s face next to a Star of David shape on top of a bed of money. Inside the star were the words “Most Corrupt Candidate Ever!”

Less than two hours later, the tweet was deleted, and the image was posted again with a circle instead of the star.

The offending image first appeared in a June 15 tweet by a user known for anti-black and anti-Muslim messages. According to the news website Mic, it was then shared June 22 on a section of the 8Chan Web forum frequented by white supremacists.

On Monday, Trump and his ­social-media director, Dan Scavino, said the image they used contained a “basic” or “sheriff’s” star.

Former White House press secretary Ari Fleischer said Donald Trump’s tweet of a Star of David image was “stupid,” but that he did not believe Trump was anti-Semitic. (Carolyn Kaster/ASSOCIATED PRESS)

“The social media graphic used this weekend was not created by the campaign nor was it sourced from an anti-Semitic site,” Scavino said in a statement. “It was lifted from an anti-Hillary Twitter user where countless images appear. The sheriff’s badge — which is available under Microsoft’s ‘shapes’ — fit with the theme of corrupt Hillary and that is why I selected it.”

But many Republicans saw the episode as part of a broader pattern of Trump retweeting messages from openly racist individuals.

“There have been too many instances. That’s what bothers people,” said Lisa Spies, a Republican fundraiser with strong ties to the Jewish community. “If it was just the tweet and he apologized, that would be one thing. Why does this keep coming up? What’s inexcusable is that it’s happening over and over again.”

Spies, who said she is having a hard time supporting Trump because of his history of offensive statements, added: “Here’s the fundamental problem: No one knows anybody on the Trump campaign. Usually donors would be talking to the director of Jewish outreach. I don’t know if they even have a director of Jewish outreach.”

Trump’s campaign said that it does not a staffer in that role right now but that it has Jewish team members and prominent Jewish supporters outside the campaign.

Ben Carson, a Trump supporter, said Tuesday on MSNBC that “it doesn’t really matter” if Trump adjusts his social-media style because he is going to face criticism anyway. “I know Donald Trump, and I know he’s not a racist by any stretch of the imagination, and that’s really what needs to be brought out,” Carson said.

But he posted a vaguely worded tweet earlier Tuesday: “Social media provides a great platform for discourse, but we must be careful with the messages we send out.”

Ari Fleischer, who served as George W. Bush’s White House press secretary and sits on the Republican Jewish Coalition’s board of directors, was blunter.

“This was stupid, and it was foolish,” Fleischer said. “Anybody who has been around politics would have instantly recognized the blunder he was making.”

But Fleischer, who plans to vote for Trump, added: “I reject the notion that he is anti-Semitic. No one who is anti-Semitic would welcome the marriage of their daughter to an Orthodox Jew,” he said, referring to Kushner.

The RJC, which has said it will work to help get Trump and other Republicans elected, has not responded to requests for comment on the tweet.

In her piece titled “An Open Letter to Jared Kushner, From One of Your Jewish Employees,” Observer writer Dana Schwartz recalls the anti-Semitic messages she received on Twitter after posting criticism of Trump’s original tweet.

“When you stand silent and smiling in the background, his Jewish son-in-law, you’re giving his most hateful supporters tacit approval,” Schwartz wrote. “Because maybe Donald Trump isn’t anti-Semitic. To be perfectly honest, I don’t think he is. But I know many of his supporters are, and they believe for whatever reason that Trump is the candidate for them.”

Matea Gold and David Weigel contributed to this report.