Donald Trump Jr.'s criticism came in response to a report that Moore said he would improve on his previous run by engaging in "more personal contact with people."
"This can't be real... can it? Based on the allegations I'd stay away from that but hey I'm new to this," Trump Jr. tweeted.
Moore announced his 2020 candidacy on Thursday despite leading Republicans criticizing him and President Trump publicly saying he couldn't win.
“Can I win?" Moore said at his announcement on Thursday. "Yes, I can win. Not only can I, they know I can. That’s why there’s such opposition."
Trump Jr. also disputed Moore's claim that he wasn't "going against" his father with his decision to run.
"This is pure fake news. I can assure everyone that by running, Roy Moore is going against my father and he’s doing a disservice to all conservatives across the country in the process," Trump Jr. tweeted on Thursday.
In May, he also mocked Moore after he teased another Senate bid. "You’re literally the only candidate who could lose a GOP seat in pro-Trump, pro-USA ALABAMA," Trump Jr. tweeted.
"Running for office should never become a business model. If you actually care about #MAGA more than your own ego, it's time to ride off into the sunset, Judge."
Republicans in Washington have made clear they don’t want Moore to run again, saying they believe any other Republican will beat Jones in 2020. The National Republican Senatorial Committee has said its motto in the race is “ABRM,” which stands for “anyone but Roy Moore.”
"We believe most Alabama Republicans realize that nominating Roy Moore would be gift wrapping this Senate seat for Chuck Schumer," Jack Pandol, a spokesman for the Senate Leadership Fund, which is aligned with Senate Majority Leader Mitch McConnell, said Thursday. "It remains to be seen whether Moore can escape his baggage without his candidacy collapsing under its own weight, regardless of what groups on the outside do."
Fox News' Alex Pappas contributed to this report.