The minister made the pledge during a heated debate in the Dáil on a bill introduced by Independent TD Clare Daly to allow abortions on the grounds of fatal foetal abnormalities.
Mr Varadkar’s stance that the Government opposed the move because it had no mandate to legislate for the reform was branded “horse shit” by Independent TD Mick Wallace.
“You didn’t have a mandate to bring in the property tax; you didn’t have a mandate to pay the unsecured bondholders,” Mr Wallace told the Dáil.
Mr Varadkar insisted the legislation was flawed and unconstitutional, but the issue needed to be addressed after the general election which must be held by spring next year.
Hw said he would be “advocating” for reform in his party, adding: “The suggestion of a constitutional convention or something along those lines might be the correct way to move forward.”
Mr Varadkar has warned that the eighth amendment of the constitution, which gives equal status to the mother and unborn, has a “chilling” effect on doctors.
The debate saw People Before Profit TD Richard Boyd Barrett tell TDs about his own family’s suffering due to fatal foetal abnormalities.
“Next Tuesday 13 years ago I had to bury my daughter Ella who was born with fatal foetal abnormalities,” Mr Boyd Barrett said.
He warned that hundreds of people would suffer the trauma of travelling abroad for a termination of a pregnancy they wanted, adding to the anguish of their situation.
Ms Daly accused the Coalition of hypocrisy on the issue as she insisted that 50 Government TDs, including most of the Cabinet, were on record saying they supported the right to choose in fatal foetal abnormality cases.
Ms Dally, who branded the current situation “barbaric”, strongly attacked 15 Labour TDs who wrote an open letter to then health minister James Reilly urging him to grant termination rights in fatal foetal abnormality cases when he was piloting the Protection of Life During Pregnancy Bill through the Dáil in 2013.
Ms Daly’s bill has caused deep tensions within the parliamentary Labour Party as many TDs want to be granted a free vote on the issue when it returns to the Dáil on Tuesday.
Fianna Fáil health spokesman Billy Kelleher called on the Government to be “brave and bold” and follow his party’s free vote stance.
Sinn Féin’s Brian Stanley said his party would abstain as the issue is to be considered at its ard fheis in Derry next month.
The Pro-Life Campaign criticised some of the language used in the Dáil debate, and said “positive benefits of perinatal hospice care” were not discussed.