Epshteyn wrote the much-maligned statement, according to a Politico report that cited an unnamed source with knowledge of the situation.
He did not immediately respond to calls and emails from Politico, and the White House press office did not respond to emails, according to the report.
The Trump administration's statement mentioned the “victims, survivors, heroes” of the Holocaust and “the innocent," but did not specifically mention the 6 million Jews killed by the Nazis, in a break from bipartisan tradition.
It drew criticism from Anti-Defamation League director Jonathan Greenblatt, who called the omission “puzzling and troubling," and Steven Goldstein, executive director of the Anne Frank Center for Mutual Respect, who condemned Trump's "vague" language.
In a statement released Monday, the United States Holocaust Memorial Museum noted that while "millions of other innocent civilians" were exterminated by Nazis, "the elimination of Jews was central."
White House press secretary Sean Spicer continued to defend the statement in a briefing Monday afternoon, and blasted those "picking on" its failure to mention Jews as "pathetic" and "nitpicking."
He argued that Trump "went out of his way to recognize the Holocaust" and said the statement "was written with the help of an individual who's both Jewish and the descendent of Holocaust survivors."
A reporter asked if Jared Kushner, the President's son-in-law and special adviser who is a Jewish descendent of Holocaust survivors, wrote the statement.
"Did I say that?" Spicer replied. "No."
"You mentioned—" the reporter pressed.
"I know what I said. I didn't say Jared's name," Spicer said. "No, I'm not getting into who wrote it, but he has several members of the Jewish faith on his senior staff."
Epshteyn emigrated to the United States from Moscow in 1993 with his Russian Jewish family.