The Abortion Rights Campaign has called on Belfast lawmakers to follow Dublin's lead
The Health Minister Simon Harris says women in the North will be able to access abortion services here.
Speaking in Belfast, Mr Harris says services will be available to all women on the island of Ireland once the legislation is introduced.
Unlike the rest of the UK, abortion remains illegal in the North unless the women's life is at risk - or there is a serious danger to her mental or physical health.
The Abortion Rights Campaign has welcomed Minister Harris's comments.
In a statement, the group says: "Although this is a welcome step, this is not a solution to the lack of abortion access in the North.
"Women and pregnant people who travel for abortion care face practical and financial barriers; although these barriers will be lessened by travelling to Dublin rather than Liverpool, they still exist.
"Minister Harris's commitment will provide another option for those who are able to travel for services, but many will be unable to travel and will be forced to continue a pregnancy against their will."
The Abortion Rights Campaign wants Members of the Legislative Assembly (MLAs) in the North to take action: "It is to the shame of successive members of the Oireachtas that people of this island have had to travel in their thousands, and continue to do so, for care that should have been accessible here.
"It is time that they, like their Dáil counterparts, recognise their failure and start to provide care to pregnant people in their own communities."