Contrary to some public statements, President Trump and his campaign staff are likely "pretty concerned" about having former Vice President Joe Biden as a potential opponent in 2020, the Federalist publisher Ben Domenech said Thursday.

"I actually think they are pretty concerned about him," Domenech said during an appearance on Fox News' "Special Report with Bret Baier."

Domenech noted that part of the concern may stem from the fact that Trump and Biden -- a Democrat who made his White House bid official Thursday morning -- appeal to some of the same types of voters.

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"I think part of that has to do with the fact that Joe Biden has clearly proven in the past to appeal to the same states that were key to President Trump in deciding the 2016 election," Domenech said. For example, Biden -- a longtime U.S. senator from Delaware, often speaks of his childhood in Pennsylvania, a state that Trump won over Hillary Clinton in 2016.

In his campaign kickoff video Thursday, Biden argued that "if we give Donald Trump eight years in the White House, he will forever and fundamentally alter the character of this nation, who we are, and I cannot stand by and watch that happen."

Nevertheless, Trump welcomed Biden to the race, calling him "Sleepy Joe" in a tweet and warning Biden to prepare for a "nasty" primary fight against a large field of other Democrats seeking the party's presidential nomination.

Domenech said Biden is a much stronger candidate than others believe he is, in particular with African-Americans.

"Personally I think the elite opinion is wrong about Joe Biden, that he actually is a much stronger candidate that they are giving credit for," Domenech said. "I think a large part of that is that he has an enormous wellspring of support among African-American voters that you do not see for a lot of the other candidates in this race. Where they might be appealing to the more 'woke' white progressive vote that I think is the loudest and shouting about a lot of different issues right now."

The Federalist publisher also said Biden will need to deal with issues from earlier in his career that his Democratic rivals will almost certainly raise.

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"The problem here for him is how does he deal with all the hits that are going to come against him from his past?" Domenech said.

"We've seen them used in lot of different ways and I think they will be deployed against him. He will have to come up with different ways to respond to the different aspects of that."