Anthony Albanese has pulled the pin on some of Labor's most controversial tax measures, announcing expanded exemptions for small businesses and scrapping the proposed 30 per cent minimum tax on discretionary testamentary trusts.

The Prime Minister made the call at a Sydney press conference on Thursday alongside Treasurer Jim Chalmers, after the government's primary vote dropped 4 per cent since the May budget. One Nation has now overtaken Labor as the nation's most popular party.

"Following the consultation that we flagged on budget night, we're announcing details to allow more small businesses access to the capital gains tax concessions," Albanese said.

Under the changes, the existing 50 per cent active asset CGT concession for small businesses will jump from $2 million to $10 million. That means an estimated 2.7 million businesses can keep claiming the discount introduced by former prime minister John Howard back in September 1999.

The government is also proposing a new tax concession for start-ups, with a consultation paper set for release later today.

On testamentary trusts — which only kick in after someone dies and let asset holders decide how income from those assets is distributed — Albanese confirmed all discretionary ones will be exempt from the planned 30 per cent minimum tax. There are about 10,500 such trusts active in Australia.

"That was clear already, but we're making it even clearer," he said.

"We're putting that matter beyond any doubt, so that all types of discretionary testamentary trusts continue to be exempt from the minimum, subject to some integrity measures that we'll consult on."

Labor's original plan would've removed the existing 50 per cent CGT discount and replaced it with inflation indexation of the cost base, plus a minimum 30 per cent tax. Indexing the cost base to inflation means investors only get taxed on the real gain when they sell an asset.

But start-ups and small businesses were alarmed because they often start with a negligible cost base. That means they'd get almost no discount under the proposed change. That would've pushed the maximum effective CGT rate from 23.5 per cent to nearly 47 per cent for anyone earning over $190,000 in the year they sell.

A snap two-day parliamentary inquiry heard that some of Australia's most successful companies would never have survived without the 50 per cent discount.

Albanese refused to say whether the backtrack was driven by backlash. Asked directly if the changes were meant to "quell the backlash", he said: "Our ranks are very supportive of this reform."

The new exemptions will cost the budget $475 million, based on indicative costings. But the three tax reforms overall are still expected to raise about $8.1 billion over the forward estimates.

Albanese insisted the feedback on the budget has been positive. He pointed to first home buyers who'll no longer compete as heavily with investors at auctions under the government's negative gearing changes.

"This Saturday when first home buyers go along to an auction, if it's an existing home, they won't be competing as much with investors," he said.

"It's in tatters because the government simply got it wrong from the start. There's no point going on with these carve-outs. Scrap it, scrap the bill, start the budget again, because they simply got it wrong," Taylor told a Sydney press conference.