He told a BBC Question Time leaders' special he would not campaign for Leave or Remain so it would allow him, as prime minister, to "credibly" carry out what the voters then decide.
UK Prime Minister Boris Johnson later asked how Corbyn could be "indifferent" on such a vital issue. But Johnson faced questions of his own about whether he could be trusted.
The Prime Minister was the fourth party leader to answer the audience's questions, with the SNP's Nicola Sturgeon and Liberal Democrat Jo Swinson also taking to the stage for 30 minutes each, the BBC reported on Friday.
Pressed on whether politic should be relied upon to tell the truth, Johnson said this was "absolutely vital". While trust was a crucial issue for voters, he argued the biggest threat to public confidence was the "corrosive" effect of Parliament trying to block Brexit.
He said the Labour, SNP and Lib Dem leaders wanted to "basically frustrate" the result of the 2016 referendum, which the public had been waiting more than three years to see delivered, by "absurdly" holding another one.
He said that the Labour leader's views seemed to have "mutated" and Corbyn's ambition to negotiate an improved agreement would be totally undermined if he did not care whether the public backed it or not.
"He is now going to be neutral on the deal he proposes to do. I don't see how he can do a deal when he is going to be neutral or indifferent."
The Conservative leader also dismissed suggestions he was trying to suppress the findings of a report into alleged Russian interference in the 2016 referendum vote as
"Bermuda triangle stuff".
"There is no evidence whatsoever, that I know of, to show any interference in any British electoral event," he said.
He insisted his party had "zero tolerance" towards Islamophobia and said he regretted any offence he had caused in articles about race during his journalistic career - including a piece in 2018 in which he likened Muslim women wearing burqas to letter boxes and bank robbers.
But he defended the right to freedom of speech and did not accept an audience member's invitation to say "sorry" for writing them.
Labour's economic plans would be "ruinous" for the country, he argued, but he also acknowledged his plan to cut national insurance bills for low-earners - expected to be the main tax announcement in the Conservative manifesto - would only have a modest impact.
On the NHS, Johnson stuck by his claims that the health service was receiving the biggest cash injection in its history.
He added: "Of course I understand that things have been tough in the NHS and understand the pressures the NHS is under. I know the massive demand the NHS faces but we can only meet that demand if we have a dynamic economy."
( With inputs from IANS )