"We think this is an unfair tax. We think it should be scrapped," Minister for Women Kelly O'Dwyer said on Channel 7. "Millions of Australian women will benefit."
NSW Treasurer Dominic Perrottet said the decision was long overdue.
"The cost to New South Wales is about $10 million a year, but for a good cause. I think it's something that should have been done some time ago," he said.
Greens Senator Janet Rice, whose own attempt to get rid of the tax stalled after passing the Senate in June, celebrated the decision.
"This is a huge win for all Australians who menstruate and shows the power of grassroots movements when we work together," Ms Rice said.
"I'm so pleased that finally, both major parties have listened to the huge groundswell of Australians who knew from the start how sexist and unfair this tax was."
"This unfair tax on sanitary products should never have existed in the first place, especially when other items like condoms and Viagra were not taxed."
However, are those who worry that scrapping the tampon tax will lead to more exemptions from the GST in the future, undermining the broader tax system.
Though he is supportive of this particular move, Liberal MP Craig Kelly warned the GST was originally designed to apply across the board before the Australian Democrats secured concessions from John Howard.
"When you carve exemptions out, there will always be a grey area about where it should be. The barbecue chicken versus the uncooked chicken. The sandwich versus the bread — the sandwich has the tax on it, the loaf of bread doesn't," Mr Kelly told Sky News.
"The tampon tax? Fair enough. They're going to move that line a little bit further. But it does open up the argument to push the line further still.
"I wouldn't want to see that line moved any further. Let's make an exemption for the tampon tax, but cut it there."
There is another big item on the agenda at today's meeting.
The government will face far more resistance when it tries to win support for its proposed changes to the way GST revenue is carved up.
Mr Frydenberg says every state and territory will be better off under his plan to introduce a floor in GST payments. Under the proposal, no state would receive less than 75 per cent of its own GST revenue, starting in the 2024-25 financial year.
"We're putting in an additional $9 billion to support the states and territories," he said.
"There will be an additional billion dollars, in perpetuity, going to the states and territories from the GST, and we are putting in a floor at 75 cents so that no state falls below that proportion of GST shared."
But some of the state treasurers, particularly those representing Labor in Queensland and Victoria, have expressed suspicion they will actually lose money.
A $4.7 billion chunk of that $9 billion figure Mr Frydenberg mentioned will go to Western Australia. The plan was hatched to protect WA from its share of the GST once again crashing to the mining boom lows of less than 30 cents in the dollar.
Victorian Treasurer Tim Pallas believes the government is trying to fix a "political problem" in the state.
"This has nothing to do with making the distribution of the GST fairer. It's about fixing the political problem Scott Morrison has in Western Australia," Mr Pallas said.
"The Prime Minister claimed that no states will be worse off. But they've provided no mechanism to ensure this is the case."
Modelling produced by his Treasury department has suggested falling iron ore prices in Western Australia and a housing downturn in Victoria and NSW could leave multiple states hundreds of millions of dollars in the red.
"This overhaul could rip nearly a billion out of Victoria — funding that could be used to deliver the vital projects and services our growing state needs," Mr Pallas said.
Queensland and New South Wales will join his push to include a safeguard in the legislation guaranteeing no state will be worse off.
Yesterday, Prime Minister Scott Morrison told reporters he didn't need the states' agreement to legislate the GST floor anyway.
"We'll be legislating that when we come back to the parliament in a few weeks," he said.
"That's the decision of the Australian parliament, it doesn't need the agreement of the states and territories."
