An agreement expected to see US President Joe Biden's son, Hunter, plead guilty to tax charges and admit a gun offence has dramatically fallen apart in court.

The plea deal, negotiated over several weeks, was likely to spare the younger Mr Biden prison time.

But a judge on Wednesday said she could not "rubber stamp the agreement".

The case marks the first time the justice department has charged the child of a sitting president.

Hunter Biden's lawyers have been given 14 days to hash out a new deal with the prosecution.

It follows a five-year investigation into the finances of the US first son, who arrived on Wednesday morning at the court in Wilmington, Delaware.

In a plea agreement announced last month, he was to be charged with two misdemeanour counts for failing to pay his taxes on time in 2017 and 2018.

He was also to admit that he had illegally possessed a gun while being a drug user, and agree to drug treatment and monitoring in lieu of a more serious felony charge and possible jail time.

But during the three-hour hearing, US District Court Judge Maryellen Noreika questioned whether the deal would also provide Hunter Biden with immunity from crimes he could be found liable for in the future.

She said the agreement contained "non-standard terms" and its proposed resolution for the gun possession offence was "unusual".

Officials with the justice department are still investigating whether Hunter Biden violated federal laws that required him to register as a foreign agent while working in China and Ukraine during his father's vice-presidency, CNN reported.

Legal teams for both sides were seen negotiating in full view of reporters inside the court in an effort to salvage the plea deal or carve out a narrower agreement.

But the hearing ended with Judge Noreika, a Trump appointee, declining to sign the deal. She gave the two parties a fortnight to reach a new agreement and brief her.

Hunter Biden, who initially offered to enter a guilty plea, ended by pleading not guilty for the timebeing.

In a statement on Wednesday, the White House said the president and first lady "love their son and they support him as he continues to rebuild his life".

"Hunter Biden is a private citizen and this was a personal matter for him," said press secretary Karine Jean-Pierre.

Republicans zone in on Hunter allegations

The misdemeanour tax counts are minor charges compared to the more serious allegations against Hunter that congressional Republicans have introduced in committee hearings.

Republicans allege that he was offered an unusually lenient plea deal because he is the president's son.

The House of Representatives Oversight Committee has already heard testimony from a whistleblower who claimed the justice department had deliberately stalled the tax investigation.

That is denied by the US Attorney for Delaware, David Weiss, who led the investigation.

Mr Weiss was appointed by former President Donald Trump and left in place by the Biden administration to finish the investigation into Hunter.

He has offered to testify in front of Congress to address criticism of the inquiry.

Republicans, who are examining various allegations against Hunter Biden, have focused on a notorious laptop that he apparently abandoned in a computer repair shop in Delaware.

The contents have been used to try to prove bribery and corruption against the president's son, and to attempt to connect his father to illegal business dealings.

But Democrats say it is no coincidence that Republicans are attacking the justice system while Mr Trump faces two criminal indictments and may soon learn of charges against him in two more cases.