australia six christmas day record rainfall
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The six, including an infant, have not been heard from since Christmas Day.
They are thought to have got stuck along a remote road in the state of Western Australia, acting Superintendent Brendan Muldoon said.
The Christmas storm drenched the usually dry region, causing flash floods and turning the soil into mud.
The Bureau of Meteorology (BOM) described it as a twice-a-century weather event, creating waterfalls all over Uluru, also known as Ayers Rock, a site sacred to indigenous people at the heart of the park in neighbouring Northern Territory.
The conditions of the roads have meant police have been unable to find the missing family, and are now using helicopters to continue their search of the area, which has no mobile phone signal.
Fears for their wellbeing were first raised after the group, who were travelling from the remote community of Kiwirrkurra, Western Australia, failed to arrive at their destination, Kintore, in the Northern Territory.
"We are seriously concerned for their welfare," Acting Supt Muldoon told reporters.
Flash floods in Kintore - where more than 232 mm (9 in) of rain fell on Monday, more than double the record December rainfall - also forced the evacuation of dozens of residents.
Northern Territory police told Australia's ABC Network that up to 25 houses were flooded in the town, near the border with Western Australia.
Papunya, another town 250km (155 miles) from Alice Springs, was completely cut off, while the town square of Yulara - the nearest community to Uluru - was inundated.
Meanwhile, a car carrying three tourists near Alice Springs was washed off a road into a flooded creek. Police have now reported all are safe.
Rangers closed the Uluru-Kata Tjuta national park at 09:00 local time on Boxing Day (23:30 GMT on Christmas Day), citing the risk of flooded roads and potential car accidents.
Parks Australia said on Tuesday that they had reopened the park but urged people to drive carefully as there was still surface water on the roads.
Uluru is a large sandstone rock in the outback sacred to the indigenous Anangu people, and one of Australia's top tourist attractions.