The Labour leader hit out at "endless offensive remarks" made by the US President, suggesting the decades-old "special relationship" could look very different under a Labour government.
The intervention came amid a furious attack from shadow foreign secretary Emily Thornberry, who called Mr Trump "an asteroid of awfulness".
"He is a danger. He is a racist," she said.
Commenting for the first time since the US leader pulled out of a visit to London to open a new embassy, Mr Corbyn was asked if Britain's relationship with the US was the most important.
"No," he told ITV's Peston on Sunday. "I think there are many important relationships.
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"The US one is obviously culturally and economically significant and important.
"The biggest disappointment of Donald Trump is, apart from his endless offensive remarks about women, about minorities and about different faiths, is his failure to support international institutions like the United Nations and like UNESCO."
Mr Corbyn also claimed a former prime minister had told him that "if they specified what the special relationship was, it wouldn't be a special relationship". He declined to say who.
The Labour leader acknowledged having a relationship with the US was important because "it is such a huge military and economic power".
New immigration minister Caroline Nokes said Britons should give Mr Trump "a good welcome" when he does visit the UK.
She denied the Foreign Office had failed over the US leader's outburst about cancelling the visit on Twitter, saying: "There was never a date set. I am sure that he will come here. We will accord, to the President of one of our greatest allies, an invitation to come here."
New Conservative party chairman Brandon Lewis told the BBC's Andrew Marr Show: "We have a hugely important relationship with the US.
"It is right that the President is welcome to the UK. It would be beneficial to us."
It comes amid a report in The Times that Mr Trump's decision to cancel the visit was for "personal reasons" after perceived slights form Theresa May and London Mayor Sadiq Khan.
A Whitehall source told the newspaper: "I don't think anyone believes this is an issue of policy or divergence between our countries."
Mr Trump announced his decision to pull out of the visit on Friday, claiming it was because the old embassy site had been sold for "peanuts" and he did not want to cut the ribbon on the new one as it was in an "off location".