Australian Treasurer Joe Hockey is to ask state and territory governments to remove the consumption tax on tampons and other sanitary products.
Earlier this month, an online petition asking the government to stop taxing a "bodily function" attracted about 90,000 signatures.
Unlike products such as condoms and sunscreen, pads and tampons attract the 10% Goods and Services tax (GST).
Mr Hockey said he would lobby state and territory governments to exempt them.
However Prime Minister Tony Abbott later downplayed Mr Hockey's pledge.
He said he understood why many people wanted to see an end to the tax, but that it was "certainly not something that this government has a plan to do".
Mr Abbott said it was up to states to decide.
In May this year, ahead of a national tax review, Sydney university student Subeta Vimalarajah started an online petition calling for an end to the tax on a "bodily function".
The petition questions the validity of taxing something most women are forced to buy every few weeks but which the government does not consider "necessary" enough to be GST-free.
"On the other hand, condoms, lubricants, sunscreen and nicotine patches are all tax-free because they are classed as important health goods," noted the petition.
"But isn't the reproductive health and hygiene of 10 million Australians important too?" it said.
Ms Vimalarajah has estimated the government raises A$25m ($20m; £13m) a year from the tax on sanitary products.
"The reason this has not been addressed already and why sanitary products were originally not exempt is either because politicians are too awkward to confront the reality of periods or they just want us to literally pay for them. Either way, it's sexist," she wrote on her blog.
During a post-budget discussion on ABC TV on Monday night, Ms Vimalarajah asked Mr Hockey if he thought sanitary products were an essential health product for half the population.
"Do I think sanitary products are essential? I think so, I think so," he replied, and said the tax "probably should" be taken off.
Mr Hockey said he would raise the issue with state treasurers at their next meeting in July.
Any changes to how GST is applied and how the revenue it raises is distributed must be supported by state and territory governments.
The tax was introduced by John Howard's conservative government in 2000, replacing various federal and state taxes.
After heated negotiation with the opposition and minor parties, most basic food items were exempted along with some education courses and medical products.
But calls for an exemption for tampons were dismissed by Mr Howard on the grounds that it would lead to too many other exemptions.