Prime Minister Rishi Sunak has denied claims he made about Labour’s tax plans were dubious despite being criticised by the UK’s statistics watchdog.

The Office for Statistics Regulation (OSR) said anyone who heard Mr Sunak say Labour’s plan would mean £2,000 of tax rises per working household would have no way of knowing that was a sum totalled over four years.

Earlier in the week, the top Treasury civil servant also objected to the Conservatives presenting their accusation as if it had been produced by impartial civil servants.

The prime minister made the claim several times during the first live TV debate with Labour leader Sir Keir Starmer on Tuesday.

Sir Keir hit back after the debate was broadcast on ITV, accusing the prime minister of “deliberately” lying about Labour’s plans, adding that he would not bring in tax rises for working people.

In an interview for ITV’s Tonight, Mr Sunak replied “no” when asked by presenter Paul Brand if he was “willing to lie in order to stay in power”.

The prime minister added that Labour were “rattled that we’ve exposed their plans to raise tax”.

Like the Conservatives, Labour has pledged not to increase the rate of income tax, National Insurance and VAT if it wins the election.

BBC Verify has analysed the Conservative’s £2,000 tax claims and concluded that they risked misleading people

In a statement released on Thursday, the statistics watchdog said the Conservatives had published a document explaining which Labour policies it had included when coming up with the number, how it interpreted the policies and how Treasury officials had costed some but not all of them.

But it added: “Without reading the full Conservative Party costing document, someone hearing the claim would have no way of knowing that this is an estimate summed together over four years.

“We warned against this practice a few days ago, following its use in presenting prospective future increases in defence spending.”

In an interview filmed for ITV’s The Leader Interviews: Rishi Sunak – due to be broadcast in full on 12 June – the prime minister denied he was willing to lie to stay in power.

Asked about his use of the £2,000 figure, he said: “I think people know that I’m across the detail when it comes to numbers.”

Ahead of the first TV debate in the run-up to polling day on 4 July, UK Statistics Authority chair Sir Robert Chote wrote to the main political parties to warn them about “ensuring the appropriate and transparent use of statistics”.

Sir Robert said: “The work of the UK Statistics Authority is underpinned by the conviction that official statistics should serve the public good.

“This means that when statistics and quantitative claims are used in public debate, they should enhance understanding of the topics being debated and not be used in a way that has the potential to mislead.”

The OSR also recently closed an investigation into a previous claim that the UK economy was “going gangbusters”, which was later referred to by officials including Rishi Sunak.

The investigation looked at whether the phrase from a top Office for National Statistics (ONS) official was taken out of context.

Mr Sunak said in an interview with the BBC’s Today programme in May: “The facts are the facts. You had, I think, the person from the Office for National Statistics talking about the economic growth that the country produced in the first quarter of the year.

“He said what he said about that and I think he used the term ‘gangbusters’, so I will leave it at that.”

Mr Sunak was quoting Grant Fitzner, the chief economist at the ONS.

Mr Fitzner had told journalists earlier in May: “To paraphrase former Australian Prime Minister Paul Keating, you could say the economy is going gangbusters.”

However, on Thursday the ONS said that it immediately clarified the comment at the time as a “passing reference” to the former Australian PM’s remarks.

A spokesperson for the ONS said: “It was certainly not intended as a comment about the overall state of the economy and when the comment was made it was immediately clarified to those present that this was not a word that the ONS would use to describe the first quarter’s growth.

“We also put the comment in context for journalists who followed up afterwards.”

Mr Fitzner’s comments came after official figures showed the economy had emerged from recession.

The ONS estimated that gross domestic product (GDP) grew by 0.6% between January and March, meaning the economy recovered from the recession recorded late last year.

The state of the UK economy is expected to be one of the key campaigning points of the general election, with leaders of various parties setting out their plans on how they would improve growth and productivity.