The Health Minister Simon Harris says it was important for him to thank the women who live tweeted their journey to England for an abortion.
The Two Women Travel Twitter account gathered 26,000 followers in a day, and made headlines around the world.
Minister Harris also says it would not be appropriate for Independent Alliance TDs to vote for a referendum abortion this autumn.
Two women, one procedure, 48 hours away from home was how the Two Women Travel twitter account described their journey to terminate a pregnancy in the UK - during which they tweeted the Taoiseach Enda Kenny, gaining huge support online - as well as receiving negative comments.
The Health Minister tweeted his thanks - saying it’s a reality which faces many, and that the matter would be discussed in a matter of weeks by a Citizens' Assembly.
Thanks to @TwoWomenTravel for telling story of reality which faces many. Citizens Assembly - a forum to discuss 8th & make recommendations— Simon Harris TD (@SimonHarrisTD) August 21, 2016
Mr Harris said: "I felt that in my role as Minister for Health that I should acknowledge the fact that they shared their experience and their story which is also the experience and story of many, many other Irish women.
"I wasn't trying to get into the specifics of the matter, just to acknowledge the fact that this had happened and that people had told their story and their experience.
"And I think that was important in terms of informing debate."
Last night, a contestant in the Rose of Tralee gave her support to the campaign to Repeal the 8th Amendment to the Constitution.
Minister Harris was asked if the Government is behind Irish society and trying to dodge the matter by letting a Citizens' Assembly consider if a referendum is needed.
Mr Harris said: "I feel that my generation, and indeed a bit older than my generation, never had a say on this matter.
"But I do feel that you have to be conscious of the fact that referenda in this country are extraordinarily difficult. You can't have a referendum based on three or four words, you have to have an informed discussion about what would people require the situation to be like in ireland."
The Irish Times reports that the Independent Alliance will seek a free vote on an abortion referendum in the Dáil in October.
Minister Harris says that would not be appropriate.
He said: "The Programme for Government very clearly sets out the process by which the 8th Amendment will be considered and that is the process of a Citizens' Assembly. Now that will get on and meet within the coming weeks, that is the process.
"I don't think therefore as a government, it is appropriate to be supporting any parallel process or any alternative process."