President Trump on Thursday struck back at Sen. Richard Blumenthal a day after the Connecticut Democrat leaked alleged details of a conversation he had with Trump’s Supreme Court pick.

Blumenthal on Wednesday told reporters that Supreme Court nominee Neil Gorsuch said previous comments made by Trump about a federal judge were “demoralizing” and “disheartening.”

“Sen. Richard Blumenthal, who never fought in Vietnam when he said for years he had (major lie), now misrepresents what Judge Gorsuch told him?” Trump tweeted.

He later added: "Chris Cuomo, in his interview with Sen. Blumenthal, never asked him about his long-term lie about his brave 'service' in Vietnam. FAKE NEWS!"

The supposed comments from Gorsuch to Blumenthal came in response to Trump’s tweet calling a federal judge a “so-called judge.” That judge had suspended Trump’s immigration restriction executive order.

But White House sources told Fox News that, while Gorsuch had indeed used the words "disheartening" and "demoralizing" during his meeting with Blumenthal, he was not specifically talking about Trump's public spat with the federal judge, and was instead speaking in generalities about attacks on the judiciary.

White House counselor Kellyanne Conway wouldn't comment on whether Trump and Gorsuch had spoken in the past day, however, she told "Fox & Friends" on Thursday that "the president is fully confident in Judge Gorsuch."

Former Sen. Kelly Ayotte, who is aiding Gorsuch as he speaks with senators, released a statement Thursday morning clarifying the comments Gorsuch made to Blumenthal.

"Judge Gorsuch has made it very clear in all of his discussions with senators, including Senator Blumenthal, that he could not comment on any specific cases and that judicial ethics prevent him from commenting on political matters," Ayotte said. "He has also emphasized the importance of an independent judiciary, and while he made clear that he was not referring to any specific case, he said that he finds any criticism of a judge's integrity and independence disheartening and demoralizing.”

Trump in his tweet latched on to Blumenthal’s history of embellishment to bolster his case that the Senate Judiciary Committee member had misrepresented Gorsuch’s remarks.

Blumenthal had for years boasted of having “served in Vietnam,” but had in actuality received five deferments, from 1965-1970, before he joined the Marine Reserve, The New York Times reported in 2010 when Blumenthal first ran for Senate. Blumenthal’s position in the Marine Reserve sent him to Washington state – thousands of miles from Asia – where he focused on local tasks, such as organizing a Toys for Tots drive.

“We have learned something important since the days that I served in Vietnam,” Blumenthal told a group of veterans in 2008, according to The Times.

Blumenthal told The Times he had misspoken, saying his “intention has always been to be completely clear and accurate and straightforward, out of respect to the veterans who served in Vietnam.”

Fox News' John Roberts contributed to this report.