World Health Organization member states agreed Tuesday to an independent probe into the UN agency's coronavirus response as US criticism mounted over its handling of the pandemic.

They also agreed to push for equitable access for any treatments or vaccines developed against COVID-19, and urged an international probe into the origins of the new virus.

Countries taking part in the WHO's annual assembly, being held virtually for the first time, adopted a resolution by consensus urging a joint response to the crisis.

The resolution, tabled by the European Union, called for an "impartial, independent and comprehensive evaluation" of the international response to the pandemic, which has so far infected more than 4.8 million people and killed more than 318,000.

It said the investigation should include a probe of "the actions of WHO and their time-lines pertaining to the COVID-19 pandemic".

The EU's foreign policy chief Josep Borrell and health chief Stella Kyriakides issued a joint statement stressing that "an independent investigation of how this pandemic started and spread will be important... to strengthen our global preparedness for the future."

WHO chief Tedros Adhanom Ghebreyesus welcomed the call for a review, stressing Tuesday that he would "initiate such an evaluation at the earliest appropriate moment."

But he insisted there was no need for a dramatic overhaul of the organisation, urging instead the global community to "strengthen, implement and finance the systems and organisations it has -- including WHO."