Leading Brexit campaigner Iain Duncan Smith has distanced himself from a pledge by the official leave campaign to spend £350m “sent to the EU every week” on the NHS, saying he had never made the claim.

During the referendum campaign, Vote Leave issued posters reading: “Let’s give our NHS the £350m the EU takes every week.” The campaign’s battlebus, outside which the former work and pensions secretary was frequently photographed, featured the slogan: “We send the EU £350 million a week – let’s fund our NHS instead.”

But asked about the statement on Sunday morning, Duncan Smith said he had never made the claim during the campaign.

Speaking to the BBC’s Andrew Marr Show, he said: “I never said that during the course of the election. The £350m was an extrapolation of the £19.1bn – that’s the total amount of money we gave across to the European Union. What we actually said was a significant amount of it would go to the NHS. It’s essentially down to the government, but I believe that is what was pledged and that’s what should happen. There was talk about it going to the NHS, but there are other bits and pieces like agriculture, which is part of the process. That is the divide up. It was never the total.”

He denied that his comments constituted a broken promise, saying: “The lion’s share of that money, the government is now able to spend. So people can say that there is more money available now for the NHS – categorically more, which is what’s required and that’s the key point.”

The repeated claim by the leave campaign that the UK could save £350m a week by leaving the EU was criticised in the run-up to the referendum, with the independent Institute for Fiscal Studies describing the figure as “clearly absurd” and estimating that Britain’s net contributions were closer to £175m a week.

Sir Andrew Dilnot, the chair of the UK Statistics Authority, twice reprimanded the campaign for using the figure, while Conservative MP Dr Sarah Wollaston said the claim that all of the money saved would go towards the health service meant she no longer felt comfortable being part of the Vote Leave campaign.

Speaking hours after the result of Thursday’s referendum was announced, the Ukip leader, Nigel Farage, said he could not promise money spent on the EU would instead go to the NHS. “I would never have made that claim, and it was one of the mistakes that the leave campaign made,” he said. “You must understand, I was ostracised by the official leave campaign and I did – as I always do – my own thing.”

A week before the referendum, pollsters working for Britain Stronger in Europe admitted that they were getting extremely worried about Vote Leave’s suggestion that £350m sent to the EU could be diverted to British priorities such as the NHS. Guardian focus groups in Brighton and Knowsley suggested many voters saw the message and believed it.

One woman in Merseyside told the group: “Just think, we could get £20bn back a year and make the country great again.”