Donald Trump has threatened to "cut off the whole relationship" with China, as tensions between the US and China continue to rise over the origins of Covid-19.

"I'm very disappointed in China. I will tell you that right now," the US President said in an interview with Fox Business. "There are many things we could do. We could cut off the whole relationship. Now if you did, what would happen? You'd save $500 billion."

It came in response to a question about whether the US should refuse Chinese nationals student visas for sensitive science areas.

The Chinese government has hit back at the President through its state-controlled Global Times newspaper, which said cutting off China "may put world peace in a dangerous position".

The report accused the President of "talking nonsense", claimed he was "bluffing and acting tough towards China to win more support", and called him a "giant baby on the brink of a meltdown".

Beijing also threatened to take Taiwan by force if the US cut China off. "China has nothing to be afraid of as 'in the past, we didn't solve the Taiwan question because we wanted to maintain the China-US relationship, and if the US unilaterally cuts it off, we can just reunify Taiwan immediately since the Chinese mainland has an overwhelming advantage to solve this longstanding problem'."

Trump has intensified his criticism of the Chinese government in recent weeks over the way it handled the disclosure of the virus, suggesting Beijing would face consequences for allowing the virus to spread.

Beijing strongly denies the charge, insisting it transmitted all available data as soon as possible to the World Health Organisation.

But Trump doubled down, insisting: "They could have stopped it. They could have stopped it in China where it came from. But it didn't happen that way."

"It's very sad what's happened to the world and to our country, with all of the deaths," he said.

The Chinese government hit back in the report, saying the US's high death toll and increasing rate of infections has seen Trump "become grumpy and more eager to blame the scapegoat – China".

US Secretary of State Mike Pompeo also took aim at Beijing on Thursday, calling for the Chinese government to stop cyber-espionage related to US research into Covid-19.

"While the United States and our allies and partners are co-ordinating a collective, transparent response to save lives, the PRC continues to silence scientists, journalists and citizens, and to spread disinformation, which has exacerbated the dangers of this health crisis," he said in a statement.

Beijing strongly rejected the accusation, calling it a smear attempt – just as it has forcefully rejected the US accusation that the virus originated in a Wuhan laboratory.

China's ambassador to Britain, Liu Xiaoming, issued a rebuttal on Sky News. "There's not any cover-up at all," he said. "China is a victim. China is not a culprit."

When asked on Fox Business what evidence there was to support that claim, Trump was less categorical than on past occasions, even appearing to dial back his assertion.