Hunter Biden, the son of the former vice-president who is at the centre of the impeachment inquiry engulfing the White House, has admitted to “poor judgment” in taking a paid position in a Ukrainian gas company – but denied doing anything wrong.

Breaking his silence over his business dealings in Ukraine and China that have become core to the investigation into whether Donald Trump tried to enlist the help of Ukraine in his re-election campaign, Biden told ABC News on Tuesday he had allowed himself to become involved in what he described as “a swamp”.

But he repeatedly denied ever discussing his foreign work with his father Joe Biden, a frontrunner in the Democratic race to challenge Trump next year.

“In retrospect I think there was poor judgment on my part,” he said. “I know I did nothing wrong at all, but it was poor judgment to be in the middle of something that is a, it’s a swamp in many ways.”

Later on Tuesday morning, Trump offered a review of Biden’s performance. It was, he said, “really bad. Now Sleepy Joe has real problems!”

Trump also attempted to tie the Biden affair to a scandal many think tipped the 2016 election his way.

“Reminds me of Crooked Hillary and her 33,000 deleted Emails,” the president wrote, “not recoverable!”

You fall down the rabbit hole and the president is the Cheshire Cat asking you questions about crazy things Hunter Biden

Hunter Biden, 49, has largely kept out of the public eye since Trump and Rudy Giuliani, the hyperactive former New York mayor commonly described as the president’s personal attorney, began peddling a conspiracy theory that the Bidens acted corruptly in Ukraine.

Trump used a 25 July phone conversation with the Ukrainian president, Volodymyr Zelenskiy, to try to instigate an official investigation into Hunter Biden’s business activities on the board of a major Ukrainian gas company called Burisma.

According to the conspiracy theory, in 2016 Joe Biden, in his official role as vice-president, forced the firing of Ukraine’s top prosecutor in order to stymie an investigation into Burisma and Hunter Biden’s role within it.

However, several top Ukrainian officials have made clear the investigation was dormant by that time and there is no evidence the younger Biden did anything illegal.

Hunter Biden told ABC coming under fire from Trump and Giuliani felt “like living in some kind of Alice in Wonderland where you are up in the real world and then you fall down the rabbit hole and the president is the Cheshire Cat asking you questions about crazy things that don’t bear any resemblance to the reality of anything that has to do with me”.

The timing of Biden’s interview has raised eyebrows, just hours before the fourth Democratic debate in Westerville, Ohio. Joe Biden will take the stage on Tuesday night at the centre of 12 Democratic candidates in the first such debate since the impeachment inquiry was launched last month.

Several Democratic strategists have questioned the wisdom of Hunter speaking out at this critical moment. The fear is that it might switch the focus away from Trump’s efforts to enlist the help of the Ukraine government and on to the president’s home ground: his unsubstantiated claims of corruption on the part of the Bidens.

Hunter Biden also used the ABC interview to deny Trump’s unfounded allegation that he made $1.5bn from his work on a Chinese investment company. He said he had made “not one cent” from that relationship.

“Look, this literally has no basis in fact,” he said.

Asked about a 2013 trip to China in which he accompanied his father on an official vice-presidential flight, he said he had gone to accompany Joe and his daughter Finnegan. He said he had not discussed any business matters at any point.

The ABC interview is part of what appears to be a coordinated attempt by both Bidens to lance the boil of the Trump/Giuliani conspiracy theories. On Sunday Hunter announced he was stepping down from the board of the Chinese investment company. He also said he would desist from any foreign contracts were his father to win the presidency.

“I have committed I won’t serve on any boards,” Hunter Biden told ABC. “I won’t work directly for any foreign entities when dad becomes president.”

Earlier in the month, Trump stood in front of news cameras and openly encouraged China to look into the activities of his political rival and son.

Also on Sunday, Joe Biden pledged that were he to win the presidential election next year no one in his family would have any business dealings with foreign companies.

He then attempted to turn the ethical spotlight back on Trump by saying that none of his relatives would “have an office in the White House” – a dig at Trump’s senior adviser, his son-in-law Jared Kushner, and his wife Ivanka Trump.