The London mayor voiced frustrations at Labour’s ongoing efforts to appeal to both Remain and Leave voters.
Europhile Mr Khan, in an interview with Italian newspaper La Repubblica, said it was time for Mr Corbyn – a known Eurosceptic during his long spell as an MP – to “provide leadership” on Brexit and stop trying to be “all things to all people”.
He said that having seen the terms of Boris Johnson’s deal and analysis of a no-deal exit, “all forms of Brexit are worse than remaining in the EU”.
He told the paper: “I’d like the Labour Party to be braver and provide leadership on this issue.
“Sometimes, saying to people who may want to leave the EU: ‘Listen, I respect you, but let me explain to you [why] I think you’re wrong and why I think we should campaign to remain in the EU. Let me explain to you why the problems you’re having with your school, with your health care, with your children’s education, with housing, is not because of EU.'”
He went on: “I think he should go a bit further and be unequivocally pro-Remain and explain to those who are Brexiteers why he disagrees with them and have the argument.”
Mr Corbyn narrowly won a Brexit vote at the party conference last month, with members backing his policy of renegotiating a deal with the EU and putting it to a public vote should he be victorious at the next election.
Remainers in the party had wanted Labour to ditch talk of supporting even a Labour-negotiated Brexit deal and come out in favour of staying in the EU.
In his interview, Mr Khan also referred to his ongoing feud with US president Donald Trump, with the mayor warning he has become a “poster boy” for the far-right.
He said: “My concern about Donald Trump is that he is actually the poster boy for far-right nativist populist movements around the world as a fact.
“You look at people here in this country, like from Britain First or Tommy Robinson.
“All these people idolise and look up to Donald Trump. He’s the poster boy.
“The reason why we should be challenging Donald Trump is not because he’s been rude to me or saying bad things about me, but because what he stands for are policies that are now mainstream.”