Up to a million fish are believed to be dead in the Darling River at Menindee as the result of a cold front killing off an algal bloom that sucked oxygen from the water.

Mr Morrison says more information is needed before the Murray-Darling Basin plan is toyed with.

"Before we start ripping up bipartisan agreements that have been very important to how we manage that area, I think it's important that we inform ourselves more," the prime minister told reporters in Fiji on Friday.

"When you deal with serious issues like this, you don't get involved in knee-jerk responses."

Bipartisanship and the absence of playing politics was vital for continuity of the river's management, he added.

Meanwhile, the Greens are pushing for a royal commission into how the river system is managed.

Greens senator Sarah Hanson-Young says her party will introduce legislation to the upper house for a royal commission when parliament resumes next month, pointing the finger at "corrupt" irrigators.

Labor is undecided on whether it would support such an inquiry, saying it wants to see the findings of another royal commission first.

Opposition Leader Bill Shorten said he wants to see the findings of a South Australian royal commission into the Murray-Darling Basin, and advice from top experts before side deciding on the next best steps.

Royal commissioner Bret Walker is due to hand his final report to the state government by February 1.

Australian Associated Press