Theresa May has repeatedly denied that the Government struck a special deal with a Tory council leader to avoid a 15% tax hike.
Jeremy Corbyn asked the Prime Minister to "explain the difference between a sweetheart deal and a gentleman's agreement" in relation to Surrey County Council's decision not to go ahead with the increase.
But Mrs May repeatedly rejected the idea that there was a "conspiracy".
She said: "The substance of what you are asking is, has there been a particular deal with Surrey County Council that is not available to other councils? And the answer to that is no."
A leaked recording revealed that David Hodge, the Conservative leader of Surrey County Council, told a private meeting that he had dealt directly with Communities Secretary Sajid Javid to tackle the council tax issue.
Mr Hodge said he had secured a "gentleman's agreement" to avoid the 15% tax hike.
But Downing Street has repeatedly denied that a "sweetheart deal" was struck with Surrey.
The tax hike issue was previously raised by Mr Corbyn in February.
Raising the issue again at Prime Minister's Questions, the Labour leader said: "The Prime Minister's response was to accuse me of peddling alternative facts.
"Could the Prime Minister explain the difference between a sweetheart deal and a gentleman's agreement?"
But Mrs May insisted no special deal had been struck.
"As I have said before, the ability to raise a social care precept of 3% is available to every council," she said.
"The issue of the retention of 100% of business rates is going to be available to a number of councils in April.
"Now let's just look at them: Liverpool, Manchester, London.
"What do we know about those? Ah, they are all under Labour control.
"So what you are actually asking me is why should a Conservative council have access to an arrangement that's predominantly currently available to Labour councils."
Mr Corbyn repeatedly pressed Mrs May on whether a one-off deal was done, but the Prime Minister's response remained the same.
She said: "If you are asking me if there was a special deal for Surrey that was not available to other councils the answer is no.
"If you are looking to uncover a conspiracy I suggest you just look behind you."
Mr Corbyn said that if the arrangements with Surrey are "so clear and above board" then Mrs May should publish details of any and all meetings between Mr Javid, the Chancellor Philip Hammond and any council leader.
Mrs May said: "The business rate retention pilot will be coming into force for a number of councils this April.
"That includes, as I have already said in answer to your earlier question, Liverpool, Greater Manchester, Greater London and some others.
"In 2019/20 it is going to be available to 100% of councils.
"For 2018/19 councils are able to apply to be part of a further pilot. That goes for all councils across the country."
Mr Corbyn said Mrs May was "unclear" about whether a deal had been done with Surrey, prompting the Prime Minister and her colleagues on the frontbench to laugh.
She said: "Can I just say to you that really you should listen to the answers I give before you ask the next question."
Ahead of Wednesday's Budget, Mr Hammond set out plans for £500 million for additional spending on schools in England, with £320 million for 140 new free schools, including new grammar schools promised by Mrs May.
Mr Corbyn demanded assurances from Mrs May that the Government will provide the extra school places needed by 2020 as he warned of a "crisis in school places".
Mrs May said: "This Government has a policy which is about increasing the number of school places but doing more than that I want to increase the number of good school places so that every child has an opportunity to go to a good school."
But the Labour leader said the Government's plans would see the "wrong schools" built in the "wrong place" as he described free schools and grammar schools as "vanity projects".