A bipartisan push has begun for a global inquiry into the origins of the coronavirus pandemic, including China's handling of the initial outbreak in the city of Wuhan.

Key points: Ms Payne said an inquiry into the outbreak should be run independently of the WHO

Ms Payne said an inquiry into the outbreak should be run independently of the WHO The WHO has faced international criticism of its handling of the pandemic

The WHO has faced international criticism of its handling of the pandemic Labor backed the push and urged the Government to secure the support of other nations

Foreign Minister Marise Payne has urged China to allow transparency in the process and does not believe the World Health Organisation (WHO) should run the inquiry.

Senator Payne told Insiders any probe of the crisis would require international cooperation.

"It will need parties, countries to come to the table with a willingness to be transparent and to engage in that process and to ensure that we have a review mechanism in which the international community can have faith," she said.

Labor has backed the push and urged the Government to secure the support of other nations.

"Given the Minister has said this, and we support her comments, it can't just be a talking point, a point in an interview," Labor health spokesman Chris Bowen said.

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"It has to be made a reality. Yes, we support it, and we would expect and trust that China would cooperate."

Meanwhile, Senator Payne refused to be drawn on whether she trusts China over its handling of the coronavirus pandemic.

"I trust China in terms of the work that we need to do together," she said.

"The issues around the coronavirus are issues for independent review, and I think that it is important that we do that. In fact, Australia will absolutely insist on that."

On Thursday, Prime Minister Scott Morrison said there had been "very valid" criticism of the WHO and the Federal Government was reviewing how it engaged with the organisation.

But he said the organisation had responded to hundreds of requests for help in the Pacific region following the coronavirus outbreak, as well as responding to other disease outbreaks in recent years.

"So, look, I know they have had their criticism and frankly I think it has been quite deserved and of course we are frustrated, but they do important work … and they do important work here in the Pacific and we will keep working with them but it won't be uncritical," Mr Morrison said.

His comments followed the United States' threat to withdraw funding for the WHO at the request of US President Donald Trump, who claimed the organisation was promoting Chinese "disinformation" about the virus.

The WHO responded by saying it regretted Mr Trump's decision and called for the world to pull together to battle the pandemic.

The US is the largest donor to the WHO, providing more than $US400 million ($631 million) in 2019, roughly 15 per cent of its budget.