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Paul Ryan during a press conference on Capitol Hill.
In an interview on conservative radio host Charlie Sykes show, the speaker referred to Trump's tweet as "ridiculous" and "anti-Semitic." Ryan also called on the presumptive Republican presidential nominee repeatedly to improve his social media communications team.
"Anti-Semitic images have no place in a presidential campaign," Ryan told Sykes.
He added: "I really believe he's gotta clean up the way his new media works."
When Sykes noted that the speaker endorsed Trump, Ryan joked that Sykes had repeatedly reminded him of this. But the speaker also said he had previously criticized Trump's initial refusal to denounce white supremacists who endorsed his campaign.
"One of the times I spoke against him was in this area where he refused to disavow white supremacists," Ryan said.
For its part, the Clinton campaign argued that the tweet was just one in a series of racially-motivated social media content propagated by Trump.
"Donald Trump's use of a blatantly anti-Semitic image from racist websites to promote his campaign would be disturbing enough, but the fact that it's a part of a pattern should give voters major cause for concern. Now, not only won't he apologize for it, he's peddling lies and blaming others," Clinton's Director of Jewish Outreach Sarah Bard said in a statement on Monday.
"Trump should be condemning hate, not offering more campaign behavior and rhetoric that engages extremists."
The Trump campaign has maintained that the image was not racially-motivated, asserting that the six-point star was meant to represent a sheriff's badge.
"These false attacks by Hillary Clinton trying to link the Star of David with a basic star, often used by sheriffs who deal with criminals and criminal behavior, showing an inscription that says 'Crooked Hillary is the most corrupt candidate ever' with anti-Semitism is ridiculous," Trump said in a statement. "Clinton, through her surrogates, is just trying to divert attention from the dishonest behavior of herself and her husband."