Krauthammer said Monday on "Special Report" hundreds of people have spoken to him as he traveled from city to city to promote "The Point of It All: A Lifetime of Great Loves and Endeavors," and have asked him what his father would think of the current political environment.
"After the hardcover edition came out last winter, I traveled around the country... to promote it and talk to admirers of my father, people who read him and watched him on TV," he said.
"It was really moving and touching for me to realize how much of an impact he had on so many people."
Krauthammer said people have told him they feel "lost" without his father, who died in 2018 at the age of 68 after a battle with cancer.
He said his father would always go to the core of a political issue and opine without regard to a particular party or ideology, but through a few basic principles.
His father, he said, strived to be truthful, without "pulling punches," or "shaping his opinions just to please someone or please public opinion."
To that extent, Baier noted then-candidate Donald Trump had an up-and-down relationship with the elder Krauthammer.
In June 2017, Trump called the late columnist "highly overrated pundit."
"As far as Charles Krauthammer, I'm not a fan of his," Trump told Fox & Friends at the time.
However, in another interview with Baier, he thanked Krauthammer for putting 'money' on him during "Special Report's" Candidate Casino.
"I saw that -- I couldn't believe it. Thank you Charles, I'm going to make you look good, Charles," Trump said.
In response, Daniel Krauthammer told Baier those two exchanges validated the way his father viewed politics and politicians.
"My father really -- as he said many times -- his job was to call a folly a folly, and it didn't matter which side that was on," he said.
"And he certainly called out President Trump many times for those follies... but he also saw overreactions on the other side.
"He separated out what was real policy difference that's valid and should be met that way, and things that really were beyond the pale and really should be criticized."
Krauthammer remarked Trump's responses in those interviews also showed people, "never knew where my dad was going to land on a certain issue."
He added his father would likely continue that practice in the present, shying away from attacking politicians' character and instead trying to have a debate on the issues.
"Trying to persuade, not to overpower -- to meet people where they began with their assumptions," he said.
In addition, one final thing his father would most definitely have a word on, his son said, was another recent development in Washington.
Last week, Charles Krauthammer's beloved Nationals baseball team completed a four-game sweep of the St. Louis Cardinals -- advancing to the World Series.
"I know he would be happy as a ten-year-old boy," Daniel Krauthammer remarked.