The BBC's Nicholas Witchell: Colleagues say she felt betrayed and angry

A statement from the newspaper said: "The editor of The Sun has apologised to Sophie Rhys-Jones for running topless pictures of her in today's edition.

"David Yelland said: 'An editorial expressing our regret will appear in tomorrow's Sun.

The BBC's Nicholas Witchell: The apology is unlikely to satisfy the Palace or Miss Rhys-Jones

"We clearly upset Miss Rhys-Jones. It's clear to me that we have caused her great distress.

"I have therefore decided to apologise to her and to the Palace. I believe this is the right thing to do

Sun widely condemned

"No more topless pictures of Miss Rhys-Jones will appear in The Sun.

"I wish her and Prince Edward the very best, although I don't expect to be invited to the wedding.' "

The apology on Wednesday evening came after it was announced that Buckingham Palace had made a formal complaint about the publication of the picture to the Press Complaints Commission (PCC).

Prince Edward's fianc�e was snapped topless with Capital Radio DJ and TV presenter Chris Tarrant while on a business trip to Spain in 1988.

The Palace condemned the publication of the picture as "premeditated cruelty", and made the complaint under Section Three of the industry's code of practice, regarding privacy.

Earlier, a Palace spokesman said: "This morning's story in The Sun is a gross invasion of privacy and cannot be regarded as in the public interest.

"It has caused considerable distress. Prince Edward and Miss Rhys-Jones are very grateful to those members of the public who have telephoned offering support, which naturally is also our immediate concern."

PCC spokesman Luke Chauveau said The Sun would be asked to justify the picture and accompanying story.

"We have received a complaint from Buckingham Palace, it is under Clause Three privacy, and we will now be investigating it in the normal way," Mr Chauveau said.

"We will be getting the publication to justify their intrusion into the individual's private life."

The Buckingham Palace complaint was the only one received so far, he added.

Kara Noble, a disc jockey with a London radio station, who took the photograph, was sacked after it was published.

Ms Noble was at the time Mr Tarrant's co-presenter and a friend of Miss Rhys-Jones.

The publication of the picture drew widespread criticism from various quarters.

A Downing Street spokesman said the Prime Minister Tony Blair had joined the Palace in condemning it.

"The freedom of the press is important, but with that freedom comes responsibility, and it is important that when media exercise that freedom they show judgement," he said.

'Taste of dirt'

Ms Noble moved from Capital Radio to rival station Heart 106.2, where she has been co-hosting the Morning Crew show.

But the station said on Wednesday that Ms Noble had been dismissed with immediate effect following the publication of the picture.

Chris Tarrant: "We were mucking about"

Mr Tarrant has also condemned the publication of the picture, and said he was taking legal action over it.

"There was never, ever the slightest hint of romance between Sophie and myself, let alone these snidey insinuations," he said.

He said he felt "totally sickened" about what had happened, and that there was a "taste of dirt" in his mouth.

And he issued a plea for people trying to "dig up dirt" on Miss Rhys-Jones to leave her alone before she became the object of the same level of media interest as Diana, Princess of Wales.

"Edward and Sophie are getting married, they are a happy young couple in love.

"They haven't done any harm to anybody and there are no skeletons in the cupboard."

'Utter betrayal'

The publication of the photograph on Wednesday comes less than a month before Miss Rhys-Jones and Prince Edward are due to marry at St George's Chapel, Windsor.

Miss Rhys-Jones is said to feel "utter betrayal" at the publication of the picture. The Daily Mail newspaper reports that she feels ''let down'' over the affair.

According to the Mail, Miss Rhys-Jones is upset that the picture has been published so close to her wedding.

Rumours of its existence have been circulating for some time.

Miss Rhys-Jones did not attend work on Wednesday at the PR company RJH, of which she is a director.

Its Managing Director Murray Harkin issued a statement saying: "I cannot express the upset and complete distress that this has caused Sophie. "This should have been the happiest occasion in her life. All her work colleagues at RJH offer Sophie and Prince Edward their full support and best wishes."