Prime Minister Scott Morrison has tested positive for Covid-19 but says he will carry on working from isolation at home as Australia's east coast battles huge floods.

The prime minister said he was suffering from "flu-like" symptoms after a PCR test came back positive on Tuesday. 

"While in isolation I will continue to discharge all my responsibilities as prime minister," he said in a statement late Tuesday.

Morrison said he would be working on the response to deadly floods in Queensland and New South Wales, "ensuring we stand with each and every one of the affected communities".

"I will also be focused on our urgent response to the tragedy unfolding in Ukraine and Russia's senseless aggression, staying in regular contact with our security and intelligence officials and our international partners."

Morrison said he had tested himself for Covid-19 on the mornings of Sunday, Monday and Tuesday, all with negative results. 

But he developed a fever late on Tuesday and tested himself again, with "inconclusive" results. A more precise PCR test then showed he was infected with Covid-19.

The prime minister said his wife and two daughters had so far tested negative but would be isolating with him at home as close contacts.