"Good," Trump replied on Twitter. "Then I think I'll do the same thing with the Fake News Networks and the Radical Left Democrats in the General Election debates!"

DNC chairman Tom Perez that the Fox News channel's close relationship with the president meant that they would not allow the cable news network to host any of their debates.

"Just to be clear, Fox News will not serve as a media partner for the 2020 Democratic primary debates," Perez said on Twitter. He said that Fox News could not host "a fair and neutral debate" for their candidates.

But Trump indicated that he might not participate in general election debates with establishment media figures.

In 2016, NBC's Lester Holt, ABC's Martha Raddatz, CNN's Anderson Cooper, and Fox News' Chris Wallace were selected by the Commission on Presidential Debates to moderate the general election debates with Hillary Clinton and Donald Trump.