George Freeman, who was May's chief policy advisor up until November last year, said that May had done an "extraordinary job" of leading "a nation which was rudderless" following the 2016 EU referendum.
However, he added that once Article 50 talks are concluded in March next year, the Conservative party must choose a new prime minister to design the UK's future relationship with the EU.
"She [May] deserves the chance to honour her promise and deliver our departure from the European Union on March 29," Freeman, the Tory MP for Mid Norfolk, told an event hosted by The Times.
"But the shape of our future relationship must be forged by a new leader. Someone liberated from the poisonous politics of the EU referendum and the shambles that has followed."
Freeman later said that May's successor should come from the Conservative party's new generation of MPs, and not someone who was heavily involved in the EU referendum campaigns, like Boris Johnson or David Davis.
"I think it needs to be led by somebody with a new mandate," Freeman — who at last year's Conservative conference warned that the party risked "electoral wipeout" — said on Thursday evening.
"I think anybody who was involved in that referendum campaign, it was a bad campaign on both sides, they are bound by all sorts of promises that shouldn't have been made, they carry the baggage of a terrible process. I think we need a new energy, a new direction, a new direction leader to take us forward, backed up by the talent that we've got."
Freeman's remarks come amid intense speculation that the Tory party's staunch Brexiteers, fronted by Jacob Rees-Mogg, are planning to trigger a leadership contest in the next few weeks in order to derail May's Brexit plans.
Over 50 pro-Brexit Tory MPs met in Parliament earlier this week, leading to talk of an imminent leadership contest. However, senior Brexiteers like Rees-Mogg have since declared their support for the embattled prime minister.
Freeman on Thursday accused MPs who were trying to oust May of being "irresponsible," telling an audience:
"People who should know better are exploiting the PM’s fragile mandate for their own success rather than for the success of the PM and the government in the negotiations. Not only is this irresponsible, it’s unnecessary."
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