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Former immigration minister Robert Jenrick has said the Conservatives suffered a "devastating" general election defeat because the party failed to deliver on its promises to the public.
He told the BBC's Sunday with Laura Kuenssberg programme the failure to cut migration was "at the heart" of the election result but he also blamed high taxes and "broken" public services.
Mr Jenrick, who is on the right of the party and has been touted as a potential Tory leadership contender, did not rule out running to replace Rishi Sunak.
However, he said the first step was getting "the right diagnosis of what's gone wrong" and talk of leadership bids was "self-indulgent" at this stage.
Also appearing on the programme, shadow health secretary Victoria Atkins, agreed "this weekend is not about leadership".
Ms Atkins did not rule out running herself but added: "We need to show the public that we understand they have sent us some very, very loud messages, that we are listening, that we are reflecting and then we as a party need to get together and unite and work out what we want for the future."
Ms Atkins, who spent just over six months as health secretary in Mr Sunak's government, is on the moderate wing of the party and has been tipped as a potential future leader.
The Conservatives now have only 121 MPs - the lowest number in the party's history after losing 251 seats in a Labour landslide.
Mr Sunak has vowed to stay on as leader until arrangements for selecting his successor are in place.
The timetable for this remains unclear and no Tories have confirmed they will run to replace him yet.
Party grandees are expected to meet next week to decide the process by which the party will choose the next leader.
Other figures tipped to run include former Home Secretary Suella Braverman, blamed the Tory defeat on an "idiotic" campaign strategy, as well as high taxes and immigration.
On Saturday, she said she had “no announcements” on whether she would run, saying the party needed to “take our time” after a “really bad result”.
Others mentioned as possible leadership contenders include former ministers Kemi Badenoch, James Cleverly, and Tom Tugendhat.
The pool of potential candidates has been reduced by the Tories' disastrous election performance, with mooted contenders Grant Shapps and Penny Mordaunt among dozens of ministers losing their seats.
Two-time previous candidate Jeremy Hunt, who served as Mr Sunak's chancellor and narrowly held his seat, is reportedly not thinking of running again.