Liz Truss’s campaign has predicted an “exodus of MPs from Sunak to us” as 10 more MPs back her leadership bid.
MP Chris Skidmore had been supporting Rishi Sunak but switched his support, saying he was “concerned by his [Mr Sunak’s] consistently changing position, especially on the economy”.
Sunak ally Theresa Villiers MP said people would “inevitably change their mind” during the campaign.
But speaking to Sky News, she said Mr Sunak had “a huge amount of support”.
The results of the contest to replace Boris Johnson as the next leader of the Conservative Party, and the next prime minister, are due to be announced on 5 September.
So far, polls have suggested that Ms Truss is more popular among Conservative Party members.
Her campaign has received a boost after 10 Conservative MPs – including minister Damian Collins – pledged their support in a letter, praising Ms Truss’s “vision and record for delivery”.
One of the signatories, Mr Skidmore, accused Mr Sunak of “consistently changing” his position on the economy to “chase votes”.
“Liz Truss has demonstrated that she has the leadership and personal ability to bring us all together,” he said.
A spokesperson for Ms Truss said: “We’re in talks with others from camp Rishi and Chris coming over could trigger a bigger exodus of MPs from Sunak to us.
“Rishi’s flip-flopping on the economy is clearly upsetting a lot of his backers.”
Last month, Mr Sunak pledged to scrap VAT on energy bills if prices keep rising, having previously opposed Labour’s plan to end the 5% rate.
Supporters of Ms Truss called this a “screeching U-turn”, but Mr Sunak’s team argued he had been consistent in trying to provide support for people struggling with bills.
In his interview with ITV News on Tuesday evening, Mr Sunak acknowledged he was “definitely the underdog” in the leadership contest but has said he is “giving it absolutely everything I’ve got”.
The former chancellor will hope to improve his fortunes when he takes part in an interview on Wednesday evening with the BBC’s Nick Robinson.
The programme – Our Next Prime Minister: The Interviews – will be broadcast at 19:00 BST on BBC One.
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