Kudlow, a confidant of President Donald Trump, spoke as stocks were falling, with the Dow Jones industrial average down more than 100 points, after a Bloomberg report said Trump is convinced Cohn will leave the administration if he follows through on his steel and aluminum tariffs.
"Personally, I have urged Gary Cohn to stay. I spoke to him this week and I said, 'please stay,'" said Kudlow, currently a CNBC senior contributor who served in the Reagan administration.
"[Cohn] and Mnuchin are the twin pillars of economic growth in this administration," Kudlow added on "Fast Money Halftime Report."
Kudlow told "Squawk Box" on Friday that Trump has done great things like tax cuts and deregulation, but the tariffs plan is not among them.
"I've had this discussion with the president," said Kudlow at the time. "I've had it for two years-plus. I won a lot of discussions on taxes, on regulations. I have not won any on trade."
On Thursday, Kudlow said Trump's tariffs are a "bad omen" and could cause a "major calamity."
Earlier on Tuesday, CNBC's Jim Cramer said the stock market is selling off on fears that top White House economic advisor could resign.
In a short tweet Tuesday morning, Cramer simply said: "Cohn sell off."