Asked to name his favorite Democrat during a television interview, Donald Trump Jr answered “Mitt Romney”, taking another swipe at one of his father’s few outspoken critics in the Republican party.

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The president’s son was appearing on CBS’s This Morning to promote his new book, Triggered: How the Left Thrives on Hate and Wants to Silence Us.

The Guardian obtained an early copy of the memoir-cum-political screed last week, reporting that it revealed the author to be “every bit as devoted to partisan trolling, childish insults and grudge-holding as his father in the Oval Office”.

On CBS, Trump Jr said he was not ruling out a run for office of his own, and said: “After what I have been through for the last few years, I probably am entitled to hit back a little bit.”

Romney, the Republican nominee for president in 2012, is the strongest GOP critic of Donald Trump in the Senate, where he represents Utah. He has called the president a “phoney”; the president has called him “a pompous ass”. Romney is a lonely voice, though, in a Senate unlikely to convict if the House votes to impeach.

On CBS, Trump Jr was confronted with a Fox News poll released last weekend, which said 49% of Americans want the president impeached and removed, over his attempts to have Ukraine investigate his political rivals in return for nearly $400m in military aid and a White House meeting.

“Listen,” Trump Jr replied, “I think you talk about reality. When you talk about what’s going on as it relates to the impeachment inquiry you have Adam Schiff who’s been a known hater.”

Schiff, a Democrat from California and the House intelligence chair, is leading the impeachment inquiry which was formalised by vote last week.

On Monday he released the first two transcripts of testimony given in private by senior state department officials about the Ukraine issue. Most observers deemed the testimony damning for the administration. More transcripts were due to be released on Tuesday.

Trump Jr continued to attack Schiff in the interview. He said: “He’s being judge, jury and executioner throughout a process where Republicans aren’t allowed to ask questions, witnesses are told not to answer those questions.”

In fact, Republican members of the House have been present in the closed-door briefings. The White House has nonetheless encouraged its officials not to comply with subpoenas to testify.

Referring to a 25 July phone call between his father and Vlodymyr Zelenskiy, the president of Ukraine, which is at the heart of the impeachment inquiry, Trump Jr told CBS: “My father put the transcript out, read it. Everything else is opinion. Read the transcript and make your decision from there.”

The White House version of the call, which shows Trump asking Zelenskiy to “do us a favour”, is in fact incomplete. Last week Lt Col Alexander Vindman, a national security staffer, testified over his concerns about the transcript, its possible alteration and efforts to keep it from going public. Romney has called the transcript “deeply troubling”.

Trump Jr said secretary of state Mike Pompeo, under pressure over the Ukraine scandal, was doing a “great job”. Asked about Rudy Giuliani, the former New York mayor and Trump emissary whose role in Ukraine policy has proved tremendously controversial, he said: “In his role, he’s outside of government that way but I think he’s doing a good job.”

“My father’s a fighter and so’s Rudy,” he said.

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Trump Jr dutifully trumpeted his father’s achievements in office, including low unemployment and prison reform.

Discussing his relationship with his father, which he addresses at length in his book, he said: “When you’ve been backed in a corner, when you’re fighting like this, when you’ve been accused of treason by half of Congress, back in that corner I realised that, ‘Hey, I fight like my father.’ We’re not going to roll over and die just because the other side wants us to.”