Dr Norman said the Government's National Objectives Framework, which comes into force in August, would allow rivers to have as much nitrogen pollution as the Yangtze River in China, and only sets a minimum standard safe enough for boating and wading.
"In other words, they think it's okay for some rivers to be so polluted you can only dip your feet in, but not put your head under," Dr Norman said.
The Greens would strengthen the National Policy Statement for Freshwater Management, and implement a National Environmental Standard for water quality and water flows in rivers - to be enforced by local councils.
Councils would have until 2020 to implement new water quality standards - among them a maximum level for pollutants including nitrate, phosphorous, zinc, and cadmium, and minimum levels for clarity and dissolved oxygen.
A standard for water flows would prohibit all further drainage of wetlands.
In defending the Government's framework, Environment Minister Amy Adams said earlier this month: "At the moment there is no requirement for any particular standard for human health. Actually putting in place a minimum requirement that at the very least every fresh water area must be safe for wading and boating is a big step forward.
"What we have done today is confirm that every council must consider whether it is appropriate to also manage for swimmability. What has to be understood is that each time we move the bar up through that ladder, it brings considerable extra cost on to communities and councils."
Dr Norman said the Greens main environmental election policy was to clean up the rivers and beaches. More policy announcements would follow in due course.
Forest and Bird said the policy was a "good step" towards cleaning up the country's lakes and rivers.
"Creating a National Environmental Standard for water quality, which would not allow lakes and rivers to become toxic to aquatic life - and that would allow people to swim - would be another very positive step," advocacy manager Kevin Hackwell said.
"Forest and Bird would like to see a commitment from the Green Party that these efforts would be properly resourced, at both central and regional government level," Mr Hackwell said.
The party's aim to not allow any more wild rivers to be dammed and management of riverbeds to be transferred to the Department of Conservation would avoid problems that had stemmed from having unprotected rivers flowing through protected national parks and conservation areas, he said.