The Commonwealth Supervising Scientist appointed to monitor the environmental impacts of the mine, Alan Hughes, has told a Senate Committee about 100,000 litres of contaminated water is leaking out of the dam every day.
Mr Hughes also told the Committee he did not see any significant reason for concern.
The Ranger uranium mine is on a lease within the boundaries of the world-heritage listed Kakadu National Park .
The minority Greens party is calling on the mining company ERA to explain how it intends to clean up the water.
The Greens Senator Scott Ludlam says he wants to know how the water will be cleaned up.
"It's a vast quantity of water, contaminated water, with processed chemicals, heavy metals, and radinuclides seeping out from underneath the tailings dam," he said.
"And we are just very concerned to know how the company plans on remediating the vast quantity of contaminated water that's seeping out from under their tailings facility.
"I think the supervising scientist and the government is being incredibly casual, telling us not to be too worried, although they couldn't say how the company would remediate it, when they would be doing that.
"They couldn't even tell us the total volume of contaminated water that had leaked away."
The mining company, ERA ,says it has a detailed plan to clean up the water.
A spokesman, David Paterson, says the contaminated water is no threat to the Park.
"We understand this issue very well," he said.
"It's well monitored, it's well understood by us and the regulators. And we have a comprehensive rehabilitation plan, to remedy any effects on the surrounding area."