About 18,000 Australians have been evacuated from flooding across New South Wales (NSW) as heavy rain continues to batter the east coast.

Days of torrential downpours have caused rivers and dams to overflow around Sydney - the state capital - and in south-east Queensland.

Officials say the "one-in-a-50-year event" may continue all week and have urged the public to exercise caution.

Prime Minister Scott Morrison has offered funds for those forced to flee.

NSW Premier Gladys Berejiklian said no deaths had been reported by late Monday - describing it as "a miracle given what we have been through".

But there has been widespread damage in the affected areas, which are home to about a third of Australia's 25 million people.Ms Berejiklian said many of the communities "being battered by the floods" had been affected by bushfires and drought the previous summer.

"I don't know any time in state history where we have had these extreme weather conditions in such quick succession in the middle of a pandemic," she said.

Emergency services have conducted at least 750 rescues, including winching people from cars. One stranded family was lifted from their flooded home by a helicopter.

Responders also saved a family with an infant from flooding in their home in Sydney's west.