"Stop tweeting and focus on running the government," Bloomberg said Tuesday on CNN's "Anderson Cooper 360".
"If there's an allegation, you have to have a competent independent investigation that will either find something wrong or remove the cloud. It is very difficult to govern when there's a cloud around you."
The billionaire businessman argued that the President needs to "prove there's nothing there," adding that "you can't just say there's nothing there."
Clinton 'never got a real message out'
Bloomberg has been associated with both the Democratic and Republican parties, but now identifies as an independent.
"I didn't vote for Donald Trump, who is a very nice guy, but I don't think he's the right person to be President of the United States for a variety of reasons," Bloomberg said.
Speaking on whether the Democrats had a message for the 2020 presidential cycle, the former three-term mayor cited messaging.
"Hillary never got a real message out," Bloomberg said.
Clinton's message was "don't vote for that guy and the gender issue, whereas, Donald had a saying, 'make America great again,'" Bloomberg added. "I don't know what again means, but 'America.' That's patriotic. And 'great' -- that's a good word."
On the issue of climate change, Bloomberg said the President's refusal to acknowledge that it's real is "embarrassing."
"No reputable person or scientist doubts that we are creating an environmental and a climate change problem," Bloomberg said.
After President Trump pulled the United States out of the Paris Climate Agreement his charitable organization, Bloomberg Philanthropies announced it would put together $15 million to "support the operations" of the United Nation's Framework Convention on Climate Change, the arm of the UN that coordinates the Paris accord.
Bloomberg said, "Is it helpful that America pulls out and the President says these things?" No, it is not helpful. Is it a disaster for the world? No, it just makes us look foolish."