The terminations would be funded by giving grants to charities to facilitate them, taking cash directly from the Women and Equalities budget.
Care fears the new scheme will undermine Northern Irish law which makes abortion illegal except where the life or mental health of the mother is in danger.
Care's Chief Executive Nola Leach said they will, despite the new announcement, "continue to advocate for women and unborn children in Northern Ireland and across the rest of the UK."
It says that 100,000 people are alive today because of the country's laws on abortion and argue that "a world which continues to pit the rights of a woman against the rights of her unborn child is not advancing human rights."
Ms Leach went on to say that "an abortion is never an easy decision to make."
She added: "We recognize that there are difficulties women face with pregnancies, especially in cases where the unborn child may be born with a life-limiting disease, but we do not believe that abortion is the answer, and that funding for a free abortion in another country is short-sighted as it neglects any mention of an offer of counselling or care for the woman."
Ministers hastily announced funding for Northern Ireland women to undergo terminations in England on the NHS in order to avoid a revolt among Conservative MPs which threatened to undermine support for the Queen's Speech.
The speech, which contains the Government's legislative plans for the next two years, passed a House of Commons ballot on Thursday with 323 votes to 309.
Meanwhile, Bernadette Smyth (pictured) from the pro-life group Precious Life, branded the measure an "outrageous attack on democracy".
She said: "On the day when the Belfast Court of Appeal ruled that it is up to the Stormont Assembly to decide on abortion law in Northern Ireland, the Government at Westminster has now decided to ride roughshod over the views of the vast majority of people in Northern Ireland."