Culture Secretary Lucy Frazer has held urgent talks with the BBC director-general after a presenter was accused of paying a teenager for sexually explicit images.
Tim Davie assured her the company was investigating the allegations “quickly and sensitively”, the minister said.
The newspaper says it is not naming the presenter for legal reasons.
The BBC has also not named the presenter, but says he will not be on air in the near future. It is not yet known whether there has been a formal suspension.
“Given the nature of the allegations, it is important that the BBC is now given space to carry out its investigation, establish the facts and take appropriate action,” Frazer said on Twitter, adding that she would be kept updated.
In the Sun on Sunday, the mother of the young person – who The Sun claims was 17 when the payments from the presenter began – said her child had used the money to fund a crack cocaine habit.
She said if the alleged payments continued, her child – now aged 20 – would “end up dead”. A sum of £35,000 is reported to have been paid.
She also claimed that a picture of the presenter in his underwear, as the sun reported Saturdayhad been taken as part of a video call with her child.
After raising their concerns with the BBC on May 19, the family said they became frustrated when the presenter remained on air and then decided to approach the sun.
They made it clear they wanted no payment for the story, the paper reported.
Following the initial Sun report, some BBC presenters took to social media to deny they were the star in question, including Rylan Clark, Jeremy Vine, Nicky Campbell and Gary Lineker.
Mr Campbell of Radio 5 Live, tweeted that he had reported an anonymous Twitter account to the police over a post in which he claimed to be a presenter.
Concerns have been raised about the BBC’s complaints process – primarily what steps were taken to question the unnamed presenter and to investigate further.
Earlier on Sunday, a number of politicians said the BBC – which says it takes any allegations “very seriously” – had questions to answer.
Shadow chancellor Rachel Reeves told the company to “get its house in order”, while Tory minister Victoria Atkins called for swift action.
Ms Reeves told the BBC’s Sunday with Laura Kuenssberg program that if the reports were true and the presenter had stayed on air for weeks after the complaint was made, “that is not good enough”.
“The BBC needs to speed up their processes,” she said, while urging the BBC to provide “greater clarity now about what on earth has gone on in this case and what they are doing to try to put it right” .
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With stories like this, BBC News journalists treat the BBC in the same way as any other organization that the news service reports on.
And as with any other organisation, BBC News has to ask BBC management or BBC services for answers and contact the BBC press office for official statements.
Occasionally, BBC journalists approach senior executives for unscheduled interviews – known as “doorsteps” in the news industry.
They are also sometimes offered interviews with management – like this one with Mr. Davie over Gary Lineker row.
And when this happens, they know they will be scrutinized inside and outside the BBC over how well they hold their boss to account.
Conservative minister Victoria Atkins described the allegations as “very, very serious” and said the BBC must act “quickly” while following the procedures “it says it has in place”.
She told Laura Kuenssberg on Sunday that at the heart of this case is a “young person… who will feel all kinds of emotions” and urges people to consider them when speaking or reporting about it.
Also on the programme, TV veteran Stewart Purvis – the former head of ITN – said the saga could damage the BBC’s desire to be known as “the nation’s trusted broadcaster”.
Asked what he would do if he worked at the company, Mr Purvis said bosses should bring together people “who know what they’re doing”.
“You need human resources, you need lawyers, you need communications people, you need the bosses of the person under scrutiny,” he said.
“You have to remember that every single email you send to each other is going to be subject to scrutiny, to become public at some point, so the pressure at the top of the BBC is enormous.”
A BBC press office spokesman said on Friday: “We take all allegations very seriously and have processes in place to proactively deal with them.
“As part of that, if we receive information that requires further investigation or investigation, we will take steps to do this. That includes actively trying to speak to those who have contacted us to seek further details and understanding of the situation.
“If we don’t get a response to our attempts or don’t receive further contact, it may limit our ability to develop things, but it doesn’t mean our inquiries stop.
“If at any time new information comes to light or is provided – including via newspapers – this will be acted upon appropriately in accordance with internal processes.”
There has been no further comment since then and BBC News has asked the press office for an update.
BBC News reports impartially on the company as a whole and is not privy to information about it before other news outlets.