Oliver Letwin is under pressure to go to Sheffield in person to apologise for suggesting he wanted to stop people from the northern city going on cheap holidays.
Council leader Paul Scriven has rejected an attempt by the Cabinet Office minister to draw a line under the affair by saying that he did not mean to cause any offence.
Mr Scriven, a Liberal Democrat, dismissed the comments as “weasel words” and demanded that Mr Letwin came personally to the city to apologise to its 550,000 inhabitants.
The row started when it emerged Mr Letwin had apparently told London Mayor Boris Johnson that he did not want to see more families in Sheffield able to afford cheap holidays.
Mr Letwin has consistently refused to say whether he made the remarks, saying that it was a private conversation.
However in a letter to Mr Scriven, he said: “Under no circumstances would I wish to cause offence to the people of Sheffield in anything that I say.”
Mr Scriven, who had earlier written to Mr Letwin saying the comments were “deeply offensive”, refused to accept the explanation and demanded that he comes to Sheffield to apologise in person.
He told The Daily Telegraph: “It is not good enough to brush aside 550,000 people who he has deeply insulted through his comments.
“As leader of the council I am not willing to accept these weasel words. This senior politician really needs to come to Sheffield to apologise.”
Mr Scriven said the private comments were now public, and he needed to “come to Sheffield to explain to the people of Sheffield why he singled them out.
“It is a gross insult to the people of Sheffield. I am not going to stand by and allow him to say things without giving a full apology”.
Nick Clegg, the Deputy Prime Minister and MP for Sheffield Hallam, increased the pressure on Mr Letwin by suggesting that he “probably wants to tread with care when he comes to visit a city that I love”.
He added: “He has now, I think, overnight become the most controversial politician in Sheffield.”
Sources close to the Liberal Democrat leader said that it was up to Mr Letwin whether he went to Sheffield to apologise. He said: “Nick completely disagrees with Oliver on this one but it is up to him.”
Any visit to Sheffield would have echoes of a similar journey north made by Boris Johnson when he was an MP and the editor of The Spectator magazine.
He went to Liverpool to apologise for an editorial in his magazine, which had criticised the people of Liverpool for wallowing in their “victim status” and overreacting to the murder of Ken Bigley
Mr Johnson, now the Mayor of London, disclosed Mr Letwin’s alleged comments at a recent meeting but did not reveal who made them.
He said: “I was absolutely scandalised the other day to hear a Government minister tell me he did not want to see more families in Sheffield able to afford cheap holidays.”
He said it was “absolutely disgraceful, a bourgeois repression of people’s ability to take a holiday”, adding: “It’s a matter of social justice.”
Prime Minister David Cameron attempted to defend his chief policy adviser, suggesting that he had been misquoted.
He said yesterday: “I normally find, if you look at the full quotation of what Oliver Letwin has said, it is often different to what was reported in the newspapers.”
Mr Letwin declined to comment on the remarks. He told reporters: “I do not ever comment on things that are alleged to have been said in private conversations, but I would never knowingly ever say anything offensive to anybody.”
A Government source said that Mr Letwin was trying to make the point that it might be better to expand airport capacity in the north of England, rather than in the south.
Mr Letwin, a former adviser to Margaret Thatcher, has developed a reputation for straight talking. Last week he told MPs that the UK was facing a “national crisis” because of less growth and unemployment. In October 2003, when he was shadow home secretary, he was forced to apologise for saying that he would rather “go out on the street and beg” than send his twins, who were then 10 years old, to his local comprehensive school.
In an interview in November 2001, he was criticised for saying that the Tories were “nowhere near” to regaining the trust of Britons in comments which were seen as admitting the party had little chance of winning the next election, held in 2005.
Earlier that year Mr Letwin had plunged the party’s general election campaign into crisis when he suggested the party might eventually cut taxes by £20billion, far more than the planned £8billion.
During the MPs’ expenses scandal in 2009, it also emerged that he had claimed more than £2,000 for a leaking pipe to be replaced under his tennis court at his Somerset home.
He also claimed hundreds of pounds from the taxpayer to have an Aga at the property serviced regularly.