Story highlights William Kristol is a persistent critic of Donald Trump

On Twitter, Trump slammed Kristol as a "dummy" and "an embarrassed loser"

Washington (CNN) Weekly Standard Editor Bill Kristol and Donald Trump on Tuesday traded fresh blows after the conservative commentator had suggested that an "impressive" independent conservative presidential candidate is forthcoming.

Speaking at a news conference in Trump Tower in New York on Tuesday, Trump repeatedly called Kristol a "loser." He said The Weekly Standard publication was "failing" and questioned Kristol's political judgment.

"He's been wrong for two years," Trump said.

Kristol soon fired back on Twitter.

"I gather Donald Trump said I'm a loser. I've won some and I've lost some, but one thing I've always tried not to be is a roaring jackass," Kristol tweeted Tuesday afternoon.