Prime Minister Anthony Albanese has dismissed a Greens demand to “tax twice as many people twice as hard” as part of changes to superannuation.

Greens economic justice spokesperson Nick McKim has called for the threshold for the concession tax rate to start at super accounts with $1.9 million — lowered from $3 million.

The minor party also wants those accounts to face a full income tax rate, instead of any concessional rate.

It follows the Albanese government last week moving to double the concessional tax rate on super balances above $3 million from mid-2025 — rising from 15 per cent to 30 per cent.

The Greens are calling for the policy to come in from July 1 this year.

Costings by the Parliamentary Budget Office show the Greens’ policy would cover a total of 210,000 people and raise $54.6 billion over the next decade.

This compares to around 80,000 people covered by the government’s model of a $3 million threshold and concessional tax rate, which would raise $2 billion in the first full year and $3.2 billion over five years.

“The Greens want Labor to eliminate all superannuation tax concessions above $1.9 million,” Senator Nick McKim said.

“Our plan would only affect the top one per cent but it would start earlier, and tax twice as many people twice as hard as Labor’s.”

Senator McKim said “fiddling at the margins” on super tax, while still going ahead with stage 3 tax cuts was “a money-go-round scheme for the rich”.

The Greens hold the balance of power in the Senate, with the government needing the support of the minor party and at least two independents to pass legislation.

• Related: Michael Pascoe: More rubbish about taxing super than you’ll find at the tip

Albanese rejects ‘different position’

However Mr Albanese was dismissive of the push, saying on Saturday morning the government had got the balance right.

“The Greens will always find a reason to try to say that what Labor’s proposing is something that they have a different position from,” Mr Albanese told reporters in Melbourne’s east during campaigning for a by-election in the marginal seat of Aston.

“But at least they’re not like the ‘no-alition’ saying no to everything,” he added in reference to the Coalition’s promise to repeal the changes.

Senator McKim said rather than using the superannuation changes to reduce debt, money would be better spent on raising income support or doubling the Commonwealth’s rent assistance.

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“We also urge Labor to direct revenue from curbing these concessions towards helping those who need it most,” he said, referring to the government’s plan to bank the savings.

The government is consulting on the changes before introducing legislation.