Education Secretary Michael Gove has apologised to council leaders over mistakes on a list of schools affected by building cuts.
The mistakes meant schools thought their plans would go ahead only for them to find out later that they would not.
Mr Gove "apologised unreservedly" to council leaders meeting in Bournemouth, saying he was sorry for the confusion.
Councils affected by the decision are threatening to take legal action.
The mistakes were on a list relating to the scrapping of the multi-billion pound Building Schools for the Future (BSF) programme in England.
Mr Gove announced on Monday that more than 700 projects would not go ahead, saying the scheme had been plagued by "massive overspends, tragic delays, botched construction projects and needless bureaucracy".
The Department for Education then published a list of 1,500 projects saying which would go ahead, which would not and which were still being reviewed.
In Sandwell, in the West Midlands, nine schools were on the approved list on Monday but by Tuesday they had found out this was a mistake and that the plans would not go ahead.
The council branded the decision "bizarre and disgraceful" and threatened legal action but after meeting Mr Gove in Bournemouth, its leader Darren Cooper said Mr Gove had promised to review his decision on the area.
Mr Gove's officials have since denied this, saying there is "no going back" but that they would look at other ways that work could be done.
At a meeting of the Local Government Association in Bournemouth, Mr Gove said: "In setting the direction of a new policy I believe is right and necessary, I failed and it was my failure to provide totally accurate information on a school by school basis, about which schools would be affected.
"I am the person responsible and accountable for that, and I do apologise.
"I wish in particular to apologise to people in those local authorities such as Sandwell that are doing such a great job, and they found that schools were wrongly informed that their building would proceed under BSF, and, sadly, it will not proceed under BSF. I want to apologise to them unreservedly."
Mr Gove made his first apology on the issue in the House of Commons on Wednesday night, amid stormy exchanges, saying he would go to Sandwell to apologise personally.
Mr Gove told MPs there had been 25 errors on the list.
The deputy leader of Sandwell Council Steve Eling told the BBC News website: "Our schools were elated on Monday thinking the building would go ahead - and on Tuesday they heard this.
"The situation is bizarre and disgraceful and it is something we will have to challenge because the impact of not going ahead on our educational facilities will be dire."
Mr Eling said the Labour-run council was challenging the Department for Education to show the criteria it used to decide which schemes would go ahead.
He suspects a political motive: "I don't think there was a mistake. I think the list deposited on Monday was the correct list and think someone looked at it and said 'Why are we funding this Labour council?'
"The reason for Building Schools for the Future, and the investment which it would bring, was to raise educational standards and it is outrageous this will have been stolen from under our noses," he added.
Labour's education spokesman Ed Balls has said the decisions on BSF were "grossly mishandled" and that Mr Gove should apologise to "hundreds and thousands of disappointed children and parents".
"He has made two apologies and he has published three different lists of schools but even since last night it turns out there are more mistakes in the list he has put out," he said.
He says the tally of errors is now 30.
The decision to axe some of the projects has brought protests from Mr Gove's own back benches.
Conservative Ian Liddell-Grainger has three schools in his West Country constituency with cancelled projects.
He is considering taking a delegation of children to lobby in Downing Street.
The NASUWT teaching union is planning to lobby parliament on BSF on Monday 19 July and is inviting other unions to join it.
General secretary Chris Keates said: "Pupils, parents and school staff across the country are not only reeling from the devastating news of their school building programmes being slashed but also from the confusion and inaccuracy surrounding which schools are in or out of the project.
"Cutting the school building projects is totally unnecessary and is jeopardising the educational future of many children and young people."
Labour had planned to spend a total of £55bn rebuilding England's 3,500 secondary schools from the time the BSF scheme began in 2004 to 2023.
But only 180 schools have been completed.
The revised list of 1,500 schools involved in BSF and their status is available on the Department for Education website, although officials say they are "still working to put things right".
The list was compiled after the new government carried out a review of BSF schemes in conjunction with Partnerships for Schools - the body charged with delivering the programme.
Government sources say the list was drawn up by PfS.
The major errors concerned the schools in Sandwell and Doncaster.
Other affected areas are Derby, Northamptonshire, Peterborough, Greenwich, Staffordshire and Bexley.
Some schemes were said not to be going ahead when in reality they were and some which were initially said to be unaffected have now been placed on a list for "further discussion".
Other errors were minor, officials say, such as misspellings.
But Mr Balls's office said the government had listed one school, Monkseaton High in Tyne & Wear, as "stopped", while it was in fact finished, open and visited by Prime Minister David Cameron last year.