Ms Bishop, speaking at a Lowy Institute online event on Tuesday, said Mr Trump should listen to the medical and scientific advice of experts rather than discussing "unproven" responses to the virus.

She also called for "calm and considered" diplomacy at the official level after Australia's relations with China deteriorated following its call for an inquiry into the coronavirus pandemic.

The former long-standing foreign minister, who served during the Abbott and Turnbull governments, said an investigation into the lessons learnt from the crisis was needed.

China should be leading an inquiry into the pandemic, she said.

"It is regrettable that it's now descended into name calling and tensions and inflammatory rhetoric, and I think the goal of Australia and China should be to reduce tensions, and it would be helpful for there to be some calm, frank engagement between our senior officials at this point, because there's no doubt there needs to be an investigation," Ms Bishop said.

She said she would have hoped that China could have led an inquiry through the UN Security Council but that in her experience, the veto power held by permanent members meant an issue like a COVID-19 inquiry can be defeated on the floor.

"If China is not prepared to cooperate with an international investigation and independent investigation without Security Council backing, there is no legal authority of which I'm aware that would enable other countries to go into China and collect evidence," Ms Bishop said.

"We need China's cooperation and support in order for there to be an international investigation and I don't believe, given my experience in some of these international forums in the past, that we can coerce anyone into accepting an investigation that they don't want to cooperate with.

"So I think some very calm and considered diplomacy behind the scenes, not through the media, is required at this point, because it's in everyone's interests that we do learn lessons from this pandemic."

Ms Bishop also called for Australia to hold discussions with like-minded countries with similarly more successful responses to the coronavirus, including South Korea and New Zealand.

"Some of these countries could step up and show what global cooperation and collaboration can look like in the absence of global leadership. I think global leadership has gone missing in action in relation to this pandemic."

The US and China had each failed to provide that leadership, she said.

"I would be doing a lot of behind the scenes talking, getting countries who have a story to tell together and sharing that information and encouraging China to take a leadership role."

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Ms Bishop, who was foreign minister during both the Obama and Trump administrations, said chronic partisanship had "come to the fore" in recent times and affected the US response to the pandemic.

Donald Trump's response to the crisis had been "unorthodox to say the least", she said.

"I think it would be preferable if he stuck to the medical and scientific advice rather than discussing some rather unproven and dangerous responses.

"The president is dealing with a significant national crisis, there's immense pressure on him, and his unorthodox approach is unsettling for many."

Ms Bishop said she would like to see after the pandemic continued support for the "international rules-based order" of multilateral organisations that managed the way nations behaved.

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