Jim Chalmers has backed down on every criticism of his plan to tax multimillion-dollar superannuation accounts more, with the revenue he had hoped to raise taking a billion-dollar hit from the changes.

The Treasurer unveiled a new version of his two-year-old plan to lower tax concessions for large superannuation balances above $3 million after Cabinet signed off on it on Monday morning.

He wants to legislate it as soon as possible and has already spoken to the Greens, who will be key to it passing the Senate.

Under the changes, earnings on balances above $3 million will be taxed at 30 per cent, instead of 15 per cent as at the moment.

A second threshold will be added so the tax lifts to 40 per cent for balances above $10 million.

Both thresholds will be indexed so they rise each year

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