The Tánaiste has told an Oireachtas Committee that there should be a third gender option on the census along with female and male.
Leo Varadkar told the Oireachtas Committee on Gender Equality that it is "definitely something the Government is open to".
The Tánaiste was responding to Green Party TD Neasa Hourigan who said that there were people who wanted to identify as non-binary in the census and were unable to do so.
He said that "there should be a third option", adding that he would have to consult "statisticians and the CSO [Central Statistics Office] as to how best to do that".
Mr Varadkar was appearing before the Oireachtas Committee on Gender Equality today to discuss the recommendations of the Citizens' Assembly on Gender Equality regarding pay and workplace conditions.
In its report, the Citizens' Assembly recommended that the State should set targets in legislation to reduce the hourly gender pay gap to 9% by 2025 and to 4% by 2030, with a view to eliminating it by 2035.
According to Eurostat data, the current gender pay gap in Ireland is 11.3%.
On Monday, a new guide for trade unions on gender pay gap reporting was launched.
Under new legislation, organisations with over 250 employees will have to report on their gender pay gaps later this year.
Businesses are required to choose a "snapshot" date of their employees in June 2022 and then report on the hourly gender pay gap for those employees on the same date in December 2022.
Employers will also be required to publish a statement setting out the reasons for the gender pay gap in their company, and what measures are being taken to address it.
The Government has overseen a "steady and sizeable increase in the share of women on the largest companies in Ireland", Mr Varadkar said.
Women accounted for 18% in 2018, and 32% in March of this year, which he said is "a significant achievement" but added that "clearly we are not there yet", and will remain "a Republic unfinished" until parity is accomplished.
Mr Varadkar said that women continue to be disadvantaged by a "promotion bias in business".
He noted that other biases are present - including on race - and advised that "we do need to see things in the round".
Women are less likely to have their own pensions, the Tánaiste said, but noting that most of those present were under 50 years of age, added that "by the time we retire pretty much every worker will have an occupational pension".
"I think it would be appropriate and right for all Government bodies to adopt the National Living Wage, which is 60% of the median earnings", he said, referring to the recent unanimous recommendation from the Low Pay Commission.
He reiterated that the Government is committed to introducing the living wage by 2027, but said that continuing strong employment was an important factor in accomplishing this in four years, with 2023 being year one.
Small employers are concerned about being able to pay it, he added.
The Tánaiste also predicted that "over the next couple of years" the Government will succeed "in dramatically bringing down the cost of public transport, the cost of chilldcare and the cost of rent".
He said that he is open to a wider availability of flexible working provisions which are currently being drawn up for parents and carers, but told Committee Cathaoirleach Ivana Bacik that sometimes people in those roles have specific needs which require special measures.
Mr Varadkar also said that "any accelerator" to increasing the number of women in politics would be welcome.
He emphasised that he has "no objections" to applying gender quotas at a local level.
While it would require some work it is "absolutely doable", the Tánaiste said.
Mr Varadkar revealed that an independent review of collective bargaining will submit its final report in a matter of weeks.
The High-Level Working Group review of collective bargaining submitted a provisional report in July 2021, after having been set up that April.
The Government expects to receive the final report in October.
"A few people want to mull it over before it gets published," he added,
The Tánaiste was responding to Bríd Smith of Solidarity-People Before Profit who accused the Government of being "a little bit lukewarm" on the issue of trade union recognition.
Additional reporting Brian O'Donovan