Rivers in the area were not expected to crest until later in the week, meaning the number of evacuees will likely increase in the coming days.
The Australian Broadcasting Corp. said Sunday that more than 3,000 residents of New South Wales have already fled their homes and at least one death has been reported.
"The message still, as floodwaters continue to move across the state is for people to be really conscious of not driving, riding or walking through floodwater," warned Murray Kear of the State Emergency Services.
The SES and other agencies have been keeping a close eye on the Jindabyne Dam in the Snowy Mountains, which opened its spillway for the first time in its history and could cause the swollen Murray River to rise higher than it already has. Officials in the downstream town of Jingellic predicted water levels in the Murray would match the levels seen in the major floods of 2010, the ABC said.