The Labour leader said the UK had to maintain many important relationships around the world, as he hit out at “endless offensive remarks” by Donald Trump about women, minorities and different faiths.
His comments came as Emily Thornberry, the shadow foreign secretary, called the US president “a danger” and “a racist”.
However, Conservative Party chairman Brandon Lewis said it was right that an invitation for a state visit had been extended to President Trump, saying Britain should be developing its relationship with the US.
Mr Corbyn, appearing on ITV’s Peston On Sunday, was asked if Britain’s relationship with the US was the most important relationship it has with another country.
The Labour leader replied: “No. I think there are many important relationships. The US one is obviously culturally and economically significant and important.
“Also the trading relationships we have around the world with obviously the EU, but also with India and China and the rest of the world are very important. Also our relationship with international institutions such as the United Nations is very 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 did acknowledge that having a relationship with and influence over the US was important “because it is such a huge military and economic power around the world”.
He added: “I’m not sure that anyone has succeeded in defining the special relationship. I’ve asked about the special relationship and I was told once, by a former prime minister I won’t name, that if they specified what the special relationship was, it wouldn’t be a special relationship.”
Last week President Trump said he was cancelling a proposed visit to open the new US embassy in London, saying the new embassy was a “bad deal”.
However, reports over the weekend have since suggested he called off his trip because he felt he had “not been shown enough love” by the British government.
Ms Thornberry, meanwhile, told BBC1’s Andrew Marr Show that Theresa May had humiliated the Queen with the controversy over inviting President Trump to the UK.