"I have to tell you, personally, I am urging Gary Cohn to stay and fight for another day. He's done a great job," said Kudlow, a longtime economist who served in the Reagan administration. Kudlow is currently a CNBC senior contributor.
There are multiple media reports casting doubt on Cohn's future in the White House after he was unable to convince Trump not to impose steel and aluminium tariffs. There's been speculation for months about whether or not Cohn may leave his post as director of the National Economic Council.
In a brief gaggle with reporters Friday morning, White House press secretary Sarah Huckabee Sanders was asked about whether Cohn is staying. "I don't have any reason to think otherwise right now." She added, "Gary was here yesterday afternoon, I talked to him in my office several times."
Sanders also said Trump is "pretty committed" to his announced new policy, saying she did not expect the 25 percent tariff on steel and 10 percent on aluminum to change.
Kudlow said on "Squawk Box" that Trump has done great things like tax cuts and deregulation, but these tariffs are not among them. On Thursday, Kudlow said Trump's tariffs are a "bad omen" and could cause a "major calamity."
Trump announced the new tariffs Thursday, sending stocks into a tailspin, reapproaching their early February lows. Dow futures were down about 200 points Friday. The president, making good on a campaign promise to protect America's trade interests, is expected to set the tariffs as early as next week.
"I've had this discussion with the president," said Kudlow. "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."
Tariffs are "prosperity killers" that will do more harm to the U.S. economy than good, Kudlow said. "Tariffs damage the user of the commodity, in this case, steel. It's a tax."
"We're going to have a group going into the Oval [Office] to see him, probably next week to talk it through," Kudlow added.
In a tweet Friday morning, Trump suggested the U.S. would come out on top if the new tariffs were to spark an international trade war.