Criticising Corbyn's role in the EU referendum campaign, Cameron during a regular weekly exchange in Parliament said, "It might be in my party's interest for him to sit there, it's not in the national interest and I would say, for heaven's sake man, go."
Achallenge to Corbyn's Labour leadership is expected following a no-confidence vote by MPs and the two possible candidates for the post including the party's deputy leader, Tom Watson, and former shadow business secretary Angela Eagle.
Despite most of his shadow Cabinet resigning and the no-confidence vote, the Labour leader has refused to step down, saying quitting would betray all the members that back him.
The UK's vote to leave the European Union last week led Labour party MPs to question Corbyn's leadership as they felt he did not do enough to campaign for a Remain vote in line with the party's view.
In Parliament, Cameron ceased upon this and said Corbyn should "reflect on" his role in the campaign, adding: "He said he put his back into it, I would hate to see him when he wasn't trying."
The former Indian-origin shadow chief secretary to the Treasury, Seema Malhotra, who had also resigned from the shadow cabinet earlier, said: "The Labour Party is bigger than any one individual. My decision is about the future of the party and how we best focus on achieving our purpose.
"I believe we now need to move forward under a new leader to rebuild confidence in Labour and start to look like a government in waiting."
Corbyn, however, has pointed to his backing among the party's grassroots, insisting that the vote by MPs had "no constitutional legitimacy".
On Monday, he had announced a reshaped shadow cabinet to replace those that had walked out but several positions in his top team remain to be filled after the mass resignations.
The shadow cabinet walkouts - in a bid to oust Corbyn - came after the sacking at the weekend of shadow foreign secretary Hilary Benn, who told Corbyn he had lost confidence in his leadership.
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