The White House has pushed back on questions about Joe Biden’s mental fitness, with the US president daring doubters in the party to either challenge him or unite behind his candidacy.

Mr Biden, 81, took the highly unusual step of calling in to a cable news show, saying: “I am not going anywhere.”

In a tense news conference later, the president’s spokeswoman rejected suggestions that he might be suffering from an undisclosed illness.

Questions about his mental acuity have intensified since a poor debate performance against Donald Trump on 27 June.

The scrutiny is unlikely to fade this week as he hosts a summit in Washington for leaders of Nato countries.

In Monday afternoon’s daily press conference, White House press secretary Karine Jean-Pierre rejected speculation that Mr Biden was being treated for Parkinson’s disease, which can cause stiff movement and slurred speech.

“Has the president been treated for Parkinson’s?” she said. “No. Is he being treated for Parkinson’s? No.”

She was responding to a question about a report in the New York Times that an expert on Parkinson’s disease had visited the White House eight times since last year.

A letter released on Monday night from Mr Biden’s doctor said the specialist in question, Dr Kevin Cannard, had been neurology consultant to the White House since 2012 and helps “thousands of active-duty members assigned in support of White House operations”.

Physician to the President Dr Kevin O’Connor also said Mr Biden had not seen a neurologist outside of his annual physical, in which he is checked by specialists from a range of medical fields.

He noted that Mr Biden’s last physical, in February, was “extremely detailed” and contained “no findings which would be consistent with any cerebellar or other central neurological disorder”.

On Monday morning, the president called in to MSNBC’s Morning Joe programme, laying down the gauntlet to critics to “challenge me at the convention” next month, or rally behind him against Trump.

It came as he sent an open letter to congressional Democrats, saying he “wouldn’t be running again if I did not absolutely believe” that he could beat the Republican challenger in November’s election.

Mr Biden’s letter said Democratic voters in the primaries have “spoken clearly and decisively” that he should be the party’s nominee.

“Do we now just say this process didn’t matter?” the letter said. “That the voters don’t have a say… I decline to do that. How can we stand for democracy in our nation if we ignore it in our own party? I cannot do that. I will not do that.”

Mr Biden also phoned Democratic donors on Monday. One source familiar with the call told CBS News, the BBC’s US partner, that the president said his strategy for the second debate against Trump in September will be “attack, attack, attack”.

Several congressional Democrats have called for Mr Biden to drop out, but late on Monday, several others rallied round the embattled president.

Left-wing New York lawmaker Alexandria Ocasio-Cortez told reporters: “The matter is closed. Joe Biden is our nominee.

“He is not leaving this race. He is in this race and I support him.”

Ayanna Pressley of Massachusetts, Maxine Waters of California, and Frank Pallone of New Jersey echoed that support for Mr Biden.

Earlier in the day, Adam Smith of Washington state became the sixth member of Congress to publicly urge Mr Biden to quit.

“We need a stronger messenger,” he told the BBC, as he panned Mr Biden’s debate performance.

“The president was completely incapable of doing something that any sort of relatively novice debater should have been able to do, and it hasn’t gotten better since then,” he added.

On Sunday, the Democratic minority leader in the House of Representatives, Hakeem Jeffries, held a group call in which several congressmen were explicit in urging Mr Biden to step aside, according to US news outlets.

They reportedly included Jerry Nadler of New York, Mark Takano of California, Joe Morelle of New York and Jim Himes of Connecticut.

Last week, Lloyd Doggett of Texas became the first Democrat in Congress to urge Mr Biden to step aside.

Trump, 78, has ridiculed Mr Biden over the debate, last week labelling his rival “broken-down”. Biden allies have expressed exasperation about the media criticism he is facing, while his Republican challenger was recently convicted in a New York hush-money case.

Amid mounting speculation over Mr Biden’s candidacy in November, the thoughts of some Democrats have turned to who could replace him.

Some party members have rallied around Vice-President Kamala Harris, who is Mr Biden’s running mate in November.

Trump has suggested the vice-president would be “better” than Mr Biden, but still “pathetic”.

During a pair of interviews last week, Mr Biden acknowledged that he had “screwed up” the debate, but later vowed that only the “Lord Almighty” could convince him to end his bid to win the White House again.