The former US vice-president is one of the Democratic front-runners in the 2020 presidential race.

His party has launched an impeachment inquiry over claims that Mr Trump illegally pressured a foreign leader to investigate Mr Biden and his son.

Mr Trump denies wrongdoing and has dismissed the probe as a "witch hunt".

On Tuesday the White House said it would not co-operate, arguing that the proceedings were unconstitutional.

Addressing supporters in New Hampshire, Mr Biden said the president had already "violated his oath of office" and "indicted himself by obstructing justice, refusing to comply with a congressional inquiry".

It was his most forceful response to date.

Previously, the former vice-president had only gone so far as to back an inquiry to gather the facts, even as his top Democratic rivals were calling for impeachment.

Shortly after Mr Biden spoke, Mr Trump hit back at "Sleepy Joe Biden" and his "failing campaign".

Why is there an impeachment inquiry?

The Democratic-led inquiry is trying to establish whether the Republican president withheld nearly $400m (£327m) in aid to nudge Ukraine's president into launching an inquiry into Mr Biden and his son.

Hunter Biden was on the board of a Ukrainian energy company, Burisma.

In a phone call on 25 July, Mr Trump asked the newly elected Volodymyr Zelensky to scrutinise the former US vice-president.

A whistleblower raised concerns about the phone call, and the Democratic leader of the House of Representatives, Speaker Nancy Pelosi, announced a formal impeachment investigation last month.

When Hunter Biden joined the firm in 2014, questions were raised about a potential conflict of interest for his father.

But there is no evidence of wrongdoing on the part of the Bidens.

On Tuesday, the White House released an eight-page letter sent to top Democrat and House Speaker Nancy Pelosi, calling the inquiry "constitutionally invalid".

It continued: "In order to fulfil his duties to the American people... President Trump and his Administration cannot participate in your partisan and unconstitutional inquiry under these circumstances."

Ms Pelosi dismissed the letter as "manifestly wrong".

A self-inflicted wound

Analysis by Jonathan Turley, legal scholar

The letter rightfully raises concerns over the lack of a House vote and the secrecy of proceedings. The Democrats have limited Republicans in their effort to question witnesses and secure material. However, that is not a legitimate basis for refusing to co-operate or supply clearly material evidence.

The letter emphasises a lack of due process in the proceedings. Yet the constitution does not expressly require anything other than a vote of the House on impeachment itself and a majority threshold for any referral of the matter to the Senate for trial.

This is a constitutional function of the highest order for Congress. There is a legitimate basis for congressional investigation under both its oversight and impeachment authority. If proven, these allegations of self-dealing could be a basis for articles of impeachment.

A president cannot simply pick up his marbles and leave the game because he does not like the other players. A refusal to co-operate with a constitutionally mandated process can itself be an abuse of power.

The letter is another avoidable self-inflicted wound by a White House that seems intent on counter-punching itself into an impeachment.

Jonathan is professor of constitutional law at George Washington University

What is impeachment?

Impeachment is the first part - the charges - of a two-stage political process by which Congress can remove a president from office.

If the House of Representatives votes to pass articles of impeachment, the Senate is forced to hold a trial.

A Senate vote needs a two-thirds majority to convict the president - unlikely in this case, given that Mr Trump's party controls the chamber.

Only two US presidents in history - Bill Clinton and Andrew Johnson - were impeached but neither was convicted and removed.

President Nixon resigned before he could be impeached.