The former Chancellor bragged that he had started changing public funding formulas to ensure more prosperous towns receive “the funding they deserve”.
The New Statesman magazine obtained a video of the speech, which was made to grassroots Conservative members in Royal Tunbridge Wells, Kent, on July 29.
Tory figures were divided over the remarks, while Labour said Mr Sunak was “openly boasting that he fixed the rules to funnel taxpayers’ money to rich Tory shires”.
His commitment to the Government’s flagship levelling up policy, which promised more investment and opportunities for areas outside London and the South East, has also been called into question.
Henri Murison, Chief Executive of Northern Powerhouse Partnership said it has been a “bad week” for levelling up.
He added: “Two candidates both speaking to the Home Counties where many of the Conservative members live and abandoning those who gave Boris Johnson his majority in the so called Red Wall.
“Investing in tackling inequalities in our cities and towns, by improving education outcomes and dealing with chronic ill health, is good for raising productivity.
“As a former Chancellor Rishi Sunak did reform the green book to ensure the North was not disadvantaged in capital spending compared to London.
“But ensuring that northern councils facing growing adult and children social care costs can also invest in addressing the causes of intergenerational poverty is something to commit to address, not celebrate having failed on.”
Mr Sunak’s campaign did not dispute the video and instead defended its content.
“Levelling up isn’t just about city centres, it’s also about towns and rural areas all over the country that need help too. That’s what he changed in the green book,” a source said.
“Travelling around the country, he’s seen non-metropolitan areas that need better bus services, faster broadband or high quality schools. That’s what he’ll deliver as Prime Minister.”
In the video, Mr Sunak told Tory supporters: “I managed to start changing the funding formulas, to make sure areas like this are getting the funding they deserve because we inherited a bunch of formulas from Labour that shoved all the funding into deprived urban areas and that needed to be undone.
Mr Sunak, who is also the MP for Richmond is North Yorkshire, is being criticised for the remarks as he attempts to make up ground against Foreign Secretary Liz Truss to win the backing of party members, who will choose the next Prime Minister.
Foreign Office minister Lord Zac Goldsmith said: “This is one of the weirdest – and dumbest – things I’ve ever heard from a politician.”
Jake Berry, chairman of the Northern Research Group of Tory MPs, said that in public Mr Sunak “claims he wants to level up the North, but here, he boasts about trying to funnel vital investment away from deprived areas”.
The MP, who is supporting Ms Truss, said: “He says one thing and does another – from putting up taxes to trying to block funding for our armed forces and now levelling up.”
But Mr Sunak’s supporters rallied around him, with Conservative Tees Valley mayor Ben Houchen arguing that Boris Johnson led the party to electoral victory on a pledge to invest in areas “that have been ignored at the expense of urban cities”.
Shadow Levelling Up Secretary Lisa Nandy said: “This leadership race is revealing the Conservatives’ true colours. It’s scandalous that Rishi Sunak is openly boasting that he fixed the rules to funnel taxpayers’ money to prosperous Tory shires.
“This is public money. It should be distributed fairly and spent where it’s most needed – not used as a bribe to Tory members.”