Former vice president Joe Biden on Wednesday night delivered his most forceful response yet to president Donald Trump’s attacks on him and his son, accusing the Trump team of waging a campaign of “lies, smears, distortions and name calling” geared at knocking him out of the presidential race.

Mr Biden made his comments during a campaign swing through Nevada after days of internal debate among his advisers over how best to refute unsubstantiated claims by the president and his personal lawyer that Mr Biden improperly assisted his son’s business ventures in Ukraine and China.

The counterattack, people close to Mr Biden said, was intended to demonstrate what he has been promising supporters for the past week: that he would not let Mr Trump “hijack” his campaign by allowing the president’s narrative to take root. It was also intended to prove, in a walk-and-chew-gum kind of way, that he could multitask even when facing withering political fire – unveiling a serious policy proposal on guns early Wednesday in Las Vegas, then pivoting to a sharp political attack by nightfall in the north.

In the speech, the former vice president said the attacks on his family were intended to divert attention from the widening impeachment inquiry into Mr Trump’s attempts to pressure Ukraine to investigate the Bidens – and he cited them as proof that the White House feared him more than any other Democratic presidential contender.

“Let me make something clear to Trump and his hatchet men and the special interests funding his attacks against me: I’m not going anywhere,” Mr Biden told a crowd of about 500 at the Truckee Meadows Community College here.

The Democrat challengers to Trump in 2020 Show all 25 1 /25 The Democrat challengers to Trump in 2020 The Democrat challengers to Trump in 2020 Bernie Sanders The Vermont senator has launched a second bid for president after losing out to Hilary Clinton in the 2016 Democratic primaries. He is running on a similar platform of democratic socialist reform Getty The Democrat challengers to Trump in 2020 Joe Biden The former vice president recently faced scrutiny for inappropriate touching of women, but was thought to deal with the criticism well and has since maintained a front runner status in national polling EPA The Democrat challengers to Trump in 2020 Elizabeth Warren The Massachusetts senator is a progressive Democrat, and a major supporter of regulating Wall Street Reuters The Democrat challengers to Trump in 2020 Amy Klobuchar Klobuchar is a Minnesota senator who earned praise for her contribution to the Brett Kavanaugh hearings Getty The Democrat challengers to Trump in 2020 Michael Bloomberg Michael Bloomberg, a late addition to the 2020 race, announced his candidacy after months of speculation in November. He has launched a massive ad-buying campaign and issued an apology for the controversial "stop and frisk" programme that adversely impacted minority communities in New York City when he was mayor Getty Images The Democrat challengers to Trump in 2020 Tulsi Gabbard The Hawaii congresswoman announced her candidacy in January, but has faced tough questions on her past comments on LGBT+ rights and her stance on Syrian President Bashar al-Assad Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Pete Buttigieg The centrist Indiana mayor and war veteran would be the first openly LGBT+ president in American history Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Deval Patrick The former Massachusetts governor launched a late 2020 candidacy and received very little reception. 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“You’re not going to destroy me,” he said to cheers from supporters, a handful of whom were wearing “Impeach 45” jerseys. “And you’re not going to destroy my family. I don’t care how much money you spend or how dirty the attacks get.”

The American people, Mr Biden said, “know me and they know him. The idea of Donald Trump attacking anyone’s credibility is a joke.”

Earlier in the day, speaking at a gun safety forum in Las Vegas, Mr Biden excoriated the president and jokingly pretended to mispronounce the last name of his personal lawyer, Rudy Giuliani, who has communicated with Ukrainian officials on Mr Trump’s behalf.

He said there was “zero, zero, zero” evidence that his family had done anything wrong.

Mr Biden’s increasingly bitter fight with Trump comes at a potential tipping point in the 2020 Democratic presidential race. Until recently, Mr Biden had been leading in most national polls since he entered the field last spring.

But senator Elizabeth Warren of Massachusetts, fueled by a highly disciplined campaign, has surged in many early-voting states.

A Monmouth University national poll released Wednesday showed Mr Biden locked in a statistical dead heat with Ms Warren, who garnered 28 per cent support from Democratic and Democratic-leaning voters to his 25 per cent, a difference within the survey’s margin of error.

At Wednesday night’s rally, Mr Biden took a swipe at some of his Democratic opponents who have accused him of focusing too much on Trump and not enough on issues facing voters.

“A lot of my opponents say we have to do more than just beat Donald Trump,” he said. “I agree. We have to do more than beat Donald Trump. We have to beat him like a drum.”

Mr Biden’s team has been alarmed by reports that Trump’s supporters plan to launch an aggressive advertising campaign to portray the former vice president as the person who had acted improperly – despite the lack of any evidence to support that claim.

And Mr Biden’s top advisers have been equally incensed by what they view as the news media’s willingness to air unsupported allegations by Mr Trump and Mr Giuliani.

The president and his lawyer have alleged that Mr Biden, as vice president, pressured the Ukrainians to force out a top prosecutor to derail an inquiry into a Ukrainian company that paid his son, Hunter Biden. But Mr Biden said Wednesday that he had been enforcing the demands of the Obama administration and other Western nations by seeking to replace the prosecutor with an official more committed to fighting corruption.

On Sunday, Anita Dunn and Kate Bedingfield, two senior Biden strategists, wrote to several major television networks asking them to stop booking Mr Giuliani on their news programmes, accusing him of spreading “debunked conspiracy theories.”

Mr Biden amplified that argument Wednesday, urging reporters to regard Trump’s statements, and his tweets, as not simply fodder for controversy but as a dangerous “abuse of power” that included enlisting foreign leaders as allies in his re-election effort.

Mr Trump, he said, is “afraid of just how badly I would beat him next November.”

The president, in his own remarks Wednesday, did not agree.

“I’d rather run against Biden than almost any of those candidates,” Mr Trump told reporters at the White House.