"They try to say 'Well, you guys got rich off your name' -- of course I did, So did Hunter," he said.
"I get it. ... A big part of who I am is because of my father and his name. And guess what? We did that as a private business, not taking advantage of my father's taxpayer-funded office."
Trump said the company his father led, the Trump Organization, made the family its money through business conducted prior to President Trump taking office, pointing to Hunter Biden receiving a plum position at a Ukrainian energy firm while his father was vice president of the United States.
In an apparent reference to a recent ABC interview, Trump said the younger Biden "couldn't even answer why he was on the board."
Of his own family's business, he continued to defend his role at the Trump Organization -- where he serves as executive vice president -- against critics.
"We did that as private industry. And when he got that office, we stopped doing those international deals to avoid the notion of impropriety," he said, claiming the media will not report his family continues to take an accounting of income from international business and reimburses the U.S. government in turn.
"What they don't talk about is that when we have international business from embassies or other countries coming in, we literally take an accounting of that and write a check back to the U.S. Treasury. They don't say that."
Looking to the future, host Dave Anthony asked Trump whether he would consider running for office like his father.
In 2017, Trump appeared to briefly consider the potential of running for office. At the time, Gov. Andrew Cuomo, a Democrat, was preparing an ultimately successful run for a third term.
He told a New York gun club at the time that, "going back to doing deals is boring after 18 months. The politics bug bit me," according to the New York Post.
Speaking with Anthony, Trump responded to that question by saying his primary focus is helping his father -- and his political allies -- get elected or reelected in 2020.