Describing the poll as a “catastrophe” for the party, the mayor of London said for the fourth time in a row Labour had “failed” to put forward a compelling case to the British public.
His remarks came after Mr Corbyn said he would quit in “the early part of next year”, in his first interview since Boris Johnson was returned to Downing Street with the biggest Tory majority in decades.
Addressing his leadership, Mr Khan said: “The Labour Party will have to change fundamentally in order to rise to these challenges and confront the new political reality we face.
“Jeremy Corbyn has said he will stand down, and this simply must now happen quickly. But the changes we have to make will not end with his leadership.
Mr Khan, who has previously been critical of the Labour leadership, continued in a statement: “If we are truly honest with ourselves, we knew in our heart of hearts that Jeremy Corbyn’s leadership was deeply unpopular with the British people and that we were extremely unlikely to form a Labour government last night.
"Labour’s shocking and repeated failure to tackle anti-Semitism, and our inability to put forward a credible and believable set of priorities for governing have made a major contribution to the scale of this defeat.”
The London mayor added that Brexit had “accelerated a fundamental shift” in British politics, and in a scathing of assessment of the state of the party, he said: “Labour now stands more politically and culturally removed than ever before from the people our party was formed to represent and that means asking ourselves some very difficult questions”.
Speaking earlier at Islington Town Hall, Mr Corbyn it was only “responsible” for him “not to walk away from the whole party”.
“The National Executive [Committee] will have to meet, of course, in the very near future and it is up to them. It will be in the early part of next year,” he added.
Earlier, some MPs and defeated candidates demanded Mr Corbyn walk away immediately – blaming him personally for the drubbing and calling for rebuilding to begin straight away.
Margaret Hodge, who held onto her London seat, tweeted: “Corbyn talking about a period of ‘reflection’. I’ve reflected. You failed. Please stand down.”
But, asked why Labour had lost so heavily, the party leader said: “I've done everything I could to lead this party.
“I've done everything I could to develop its policies, and since I became leader the membership has more than doubled and the party has developed a very serious and fully costed manifesto.
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