Jeremy Corbyn and John McDonnell have apologised over Labour's "catastrophic" defeat in Thursday's election, which saw them lose 59 seats.
Mr Corbyn said he was "sorry that we came up short", while Mr McDonnell told the BBC he "owns this disaster".
The leader and shadow chancellor said they would step down in the new year.
The race for their replacements has already begun, with Wigan MP Lisa Nandy saying for the first time she was "seriously thinking about" running.
Mr McDonnell said it would be up to Labour's National Executive Committee to decide the mechanics of the leadership election, but he expected it to take place in eight to 10 weeks' time.
Labour suffered its worst election result since 1935 on Thursday and saw its vote share fall by eight points.
The Conservatives won a Commons majority of 80 - the party's biggest election win for 30 years - sweeping aside Labour in its traditional heartlands.
Mr Corbyn apologised to Labour supporters in two articles in the Sunday papers, calling it a "body blow for everyone who so desperately needs real change in our country".
Writing an open letter in the Sunday Mirror, he said he took his "responsibility" for the result, but insisted he remained "proud" of the party's campaign.
He doubled down in the Observer, saying his own election campaign had successfully re-set the terms of debate and his manifesto would be seen as "historically important".
But Mr McDonnell has argued "it's on me" as he apologised for the performance, on the BBC's Andrew Marr Show.
The shadow chancellor said he was sorry for "not being able to articulate" the party's campaign message ahead of the poll.
However, he also blamed the "media portrayal" of Mr Corbyn, saying "of course the system will throw the kitchen sink at you" if you challenge it.
Former Labour MP Caroline Flint - who lost her seat on Thursday - placed much of the blame at the leadership's door.
She also criticised the party's position on Brexit for leaving some voters behind, telling Sky's Sophy Ridge that "ardent Remainers", such as shadow Brexit secretary Sir Keir Starmer and shadow foreign secretary Emily Thornberry, "contributed to sacrificing" seats.
She accused Ms Thornberry of telling one her colleagues from a Brexit-backing area: "I'm glad my constituents aren't as stupid as yours."
Ms Thornberry has not yet responded to the comment.
Ms Flint added: "I don't believe anybody who have been the architects of our European policy in the last few years is credible to be leader. I don't think they can win back these seats."
Instead, she said Ms Nandy and shadow business secretary Rebecca Long-Bailey were "worth looking at".
Ms Nandy told the BBC's Andrew Marr she was considering a leadership bid after the "most shattering" defeat for Labour.
"In towns like mine, the earth was quaking as the entire Labour base crumble beneath our feet," she added.
Ms Nandy made a number of proposals - including moving the party's headquarters out of London - to help "rebuild that coalition" between "the Lewishams and the Leighs", and to regain a Labour Party that "speaks for both".
A number of other candidates are expected to join the race, including Salford and Eccles MP Ms Long-Bailey and Birmingham Yardley MP Jess Phillips.
Ms Phillips wrote in the Observer an appeal to people to join Labour to change it, arguing too many working-class people do not believe the party is better than the Tories.
Asked about the contenders, Mr McDonnell said he would "prefer others" to Ms Phillips, naming Ms Long-Bailey, shadow education secretary Angela Rayner and shadow women's and equalities minister Dawn Butler as possibilities.
He said Ms Phillips was "really talented", but added: "I want someone who actually has been really solidly involved in the development of existing policy - that's why Becky and Angie and Dawn and others have been so good."
Mr McDonnell said it "should be a woman leader next" and was "most probably time for a non-metropolitan" leader, adding: "I think it is time for a non-London MP, we need a northern voice as much as possible."
Shadow justice secretary Richard Burgon also backed Ms Long-Bailey and said he was considering running to be her deputy.
"Colleagues have approached me about that," he told Sky.
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2019-12-15 10:12:24Z
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