Donald Trump has responded to Joe Biden's announcement he will run for the Democratic presidential nomination by mocking the veteran politician's intelligence and claiming he will compete against "very sick" rivals with "demented ideas".

"Welcome to the race Sleepy Joe. I only hope you have the intelligence, long in doubt, to wage a successful primary campaign," Mr Trump tweeted on Thursday morning.

"It will be nasty - you will be dealing with people who truly have some very sick & demented ideas. But if you make it, I will see you at the Starting Gate!"

The president's jibe followed a series of tweets in which he raged against findings in the explosive Mueller report, and came just hours after the former vice-president officially announced his candidacy.

Mr Biden, who has become the instant Democratic frontrunner alongside Bernie Sanders, launched his campaign with an explicit focus on countering Mr Trump's presidency.

The 76-year-old lifelong politician warned in a three-minute announcement video handing Mr Trump a further four years in the White House would "forever and fundamentally alter the character of this nation".

He also attacked the president for his response to a white supremacist rally in Charlottesville, Virginia, in 2017, accusing Mr Trump of having "assigned moral equivalence between those spreading hate and those with the courage to stand against it".

“In that moment, I knew that the threat to this nation was unlike any I had ever seen in my lifetime,” he added.

At least 20 Democrats have put their names in the hat for the chance to take on Mr Trump next year, while several lesser-known candidates may still join the race.

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But Mr Biden is considered by many Republican activists to be the biggest threat to Mr Trump. The former vice-president is set to take a more centrist position to that of his Democratic rivals, who Mr Trump has long sought to cast as members of the "radical left".

"Amtrak Joe" – a moniker he earned for commuting daily to the US capital by rail during his time as senator – will hope to capitalise on his down-to-earth manner and blue-collar upbringing if he is to win the Democrat nomination.

He remains one of the most recognisable names in US politics, but as an older white man who spent a half-century in Washington, it is unclear if he will be embraced by an increasingly liberal Democratic Party.

Donald Trump taunts Biden amid sexual misconduct accusations as two more women come forward to accuse the democrat

He has also been dogged by questions about his past, including recent claims he touched women in an overly familiar manner without their consent.

The controversy sparked one of the most bizarre tweets of Mr Trump's presidency, when he posted a doctored video of Mr Biden sneaking up on himself.