Former Vice President Mike Pence's national security adviser Keith Kellogg -- who endorsed Donald Trump's reelection campaign on Tuesday -- urged Pence to finish certifying the 2020 election "TONIGHT" while the US Capitol was still secured during the January 6, 2021, insurrection.

Kellogg's private comments became public when a top Pence aide, Marc Short, read aloud from the email exchange in an interview Tuesday with CNN's Wolf Blitzer on "The Situation Room."

In the email, Kellogg told Short he would "recommend you stay on Hill and finish the Electoral College issue TONIGHT." When Short replied that this was their intention, Kellogg said it was "not a good... but a GREAT plan" and further encouraged Pence to "close this thing out."

These private comments sharply diverge from what Trump and his team wanted Pence to do that night. Trump allies Rudy Giuliani and John Eastman asked Pence and GOP lawmakers to further delay the Electoral College certification even after the riot was quelled, according to the federal indictment against Trump, as well as evidence uncovered by the House select committee that investigated January 6.

"On January 6th, Keith was clearly supporting the vice president's actions," Short said in the CNN interview. "I know that he's still on Donald Trump's payroll and perhaps that's why he's saying something different today."

Kellogg attorney John Coale told CNN that Short's comments in the interview were "BS." Kellogg added in a post on "X," formerly known as Twitter, that Short "failed" Pence the day of the attack.

The public war of words between Kellogg and Pence's camp erupted earlier Tuesday, when Kellogg endorsed Trump instead of Pence, who is also running for the Republican presidential nomination.

On Truth Social, Kellogg said he was disappointed in Pence's "recent actions regarding President Trump" -- likely a reference to Pence's recently ramped-up criticism of the former president, in the wake of the criminal charges against Trump in connection with January 6.

"Pence has often chosen the passive route, avoiding confrontation. This lack of assertiveness combined with an overreliance on failed political consultants like Marc Short has demonstrated a laissez-faire leadership style unworthy of the presidency," Kellogg said in the online post.

The tension between Trump and his former vice president has been a consistent narrative of the GOP primary race. Pence's team announced on Monday that he had met the criteria to qualify for the first Republican debate, which will take place on August 23. It remains unclear if Trump -- who has a commanding lead in the polls -- will show up.