The President's comments came as he continued to spar long distance with Gov. Jay Inslee (D) of Washington State, and Gov. Gretchen Whitmer (D) of Michigan.
Inslee has already been a frequent target of the President - who referred to him in one briefing as a 'snake' - acknowledging that he has urged Vice President Pence not to call the Washington Democrat.
"I say Mike, don't call the Governor of Washington, you're wasting your time with him," Mr. Trump said. "Don't call the woman in Michigan."
In an interview Thursday night with Sean Hannity on Fox News, the President took aim at Whitmer, who has complained of troubles in getting medical supplies for hospitals to combat the virus outbreak.
"We’ve had a big problem with the young, a woman governor, you know who I’m talking about from Michigan," the President said.
While Gov. Whitmer went on TV to respond to the President, Inslee used Mr. Trump's favored mode of social media.
"I’m not going to let personal attacks from the president distract me from what matters: beating this virus and keeping Washingtonians healthy," Inslee tweeted.
While Inslee avoided barbs from the White House on Friday night, Whitmer did not.
“Governor, Gretchen “Half” Whitmer is way in over her ahead, she doesn’t have a clue,” the President tweeted.
Michigan has become a flash point in recent days in the fight to stop the Coronavirus; 32 deaths were announced on Friday, almost as many as the two previous days combined.
28 deaths were announced on Friday in Washington State, raising the death toll there to 175 people, second most of any state.