David Cameron has given his full backing to the Duke of York in his role as a UK trade envoy, hours after No 10 sources questioned the prince's future.
The prime minister's spokesman said there was no review of his post and Mr Cameron had "full confidence" in him.
Prince Andrew has been criticised over his friendship with Jeffrey Epstein, a convicted sex offender and financier.
Downing Street sources had told the BBC the prince might have to step down if any more damaging revelations emerged.
BBC political correspondent Gary O'Donoghue said a Downing Street source had conceded one more serious story could make the prince's role untenable.
The Downing Street source described the recent flurry of stories surrounding the Duke of York as the media trying to create "guilt by association" but added that one more serious story could change the situation overnight.
"It's unlikely the government would actually sack Prince Andrew but may choose in the long run gradually to downgrade his activities, avoiding a damaging and embarrassing row between ministers and the Royal Family," our correspondent said.
'Guilt by association'
Mr Cameron's official spokesman said later on Monday: "We fully support Prince Andrew in his role as trade envoy. Our position is very clear. There is no review of his role."
He said the prime minister would not comment on unattributable briefings and he did not know where they came from.
Other ministers and officials have defended the prince's work, adding that it is regularly reviewed.
Chancellor George Osborne said he had been doing a "good job" promoting British exports, while Labour leader Ed Miliband said when he was in government he had seen the prince do an "effective job".
Sir Andrew Cahn, former head of the government trade body UK Trade and Investment, said the prince added "enormous value".
"He is the sort of resource that our competitors would give their eye teeth for," Sir Andrew told BBC Radio 4's World at One show.
"He has access at the highest level in markets, he is there for the long term and he has a status which other trade representatives don't have."
Earlier, Business Secretary Vince Cable said the prince would have to judge his own position, although there would be "conversations" about his future role.
"I think we need to remember he is doing this as a volunteer, he is not a government appointee, he is not somebody who is appointed and sacked," Mr Cable told the BBC.
"The assessment of the businesses I have seen that have worked with him is that he has been supportive and helpful."
One review of Prince Andrew's role took place last Tuesday when he met Sir Jon Cunliffe, the prime minister's chief adviser on Europe and overseas business.
The prince has been the UK's Special Representative for International Trade and Investment since 2001, with the job of promoting Britain's business interests around the world.
His friendship with Mr Epstein, who was sentenced to 18 months in prison in 2008 for soliciting a minor for prostitution, has been the source of an increasing number of newspaper stories and media questions.
'Error of judgement'
His judgement has also been questioned for holding meetings with Libyan leader Col Muammar Gaddafi's son Saif and for entertaining the son-in-law of Tunisia's ousted president at Buckingham Palace.
On Monday, while visiting the headquarters of London's new Crossrail in Canary Wharf, he refused to answer when BBC Newsnight reporter Michael Crick shouted: "Are you an embarrassment, sir?"
The London Evening Standard, meanwhile, quoted the Duchess of York admitting to a "gigantic error of judgement" for accepting £15,000 from Mr Epstein to help pay off her debts.
She strongly defended her former husband over the controversy surrounding his friendship with the US financier, and said he "does not know how to tell an untruth or behave dishonourably".
Labour peer and businessman Lord Berkeley told the BBC it seemed that Prince Andrew "hasn't taken very good judgement over what relationships he should build with whom".
Former Labour minister Ben Bradshaw criticised the government's handling of the row and the anonymous way Downing Street had commented on the story.
He told the BBC: "The prime minister should get a grip. It's simply unacceptable... for this drip-feed to be encouraged by No 10 in these anonymous briefings while at the same time saying officially 'Oh, he's secure in his position, there's nothing we can do'."
Meanwhile, Labour MP and foreign affairs select committee member Mike Gapes said the prince should quit.
He told BBC Two's Daily Politics show: "Once you become the story, and he becomes an embarrassment to the Royal Family, then frankly it's time for him to go."