After official results showed more than two-thirds of voters backed repealing the ban, Varadkar says he wants to make sure there are fewer crisis pregnancies and better sex education in schools going forward. As a result, thousands of Irish women make the trip overseas, often to England, to have an abortion.
Once votes from all 40 constituencies were counted, the final total indicated 66.4 percent of voters cast ballots to repeal the country's eighth amendment to its constitution in Friday's referendum, Irish broadcaster RTE reported.
Abortions are now only legal in Northern Ireland if the life or mental health of the mother is at risk.
Ireland's Minister for Children and Youth Affairs Katherine Zappone said Saturday she is confident new abortion legislation can be approved by parliament and put in place before the end of the year.
Mr Little said while Ireland's circumstances were quite different - the result of its referendum did indicate attitudes and values towards abortion were changing.
"Like many of you I am brokenhearted about the apparent result, and it's many implications, which go way beyond abortion", John McGuirk, the communications director for "Save the 8th" group that campaigned against amending the law, wrote on Facebook.
The landslide vote, celebrated outside Parliament Saturday, shows an overwhelming desire for change in a country once so closely entwined with Catholic tradition. The group said on its website that the referendum's outcome was a "tragedy of historic proportions," but McGuirk said the vote must be respected.
The government proposes that women be allowed to terminate pregnancies in the first 12 weeks.
"It's incredible. For all the years and years and years we've been trying to look after women and not been able to look after women, this means everything", said Mary Higgins, obstetrician and Together For Yes campaigner. The once conservative nation voted "yes" to repeal a constitutional ban on abortion.
A huge 66.4 per cent chose to repeal the controversial Eighth Amendment on Friday, after months of campaigning gripped the country. But I believe we have voted today for the next generation.
No social issue has divided Ireland's 4.8 million people as sharply as abortion, which was pushed up the political agenda by the death in 2012 of a 31-year-old Indian immigrant from a septic miscarriage after she was refused a termination.
Sir Vince said the United Kingdom government should take advantage of the current lack of a devolved administration in Northern Ireland.
Savita's family have been campaigning for the repeal, and her father Andanappa Yalagi said last week, "I strongly feel that the younger daughters of Ireland should not have the fate of Savita".
The support for lifting the ban highlights the liberalization of traditionally Catholic Ireland, marking the diminishing influence of the Church hierarchy and a desire to align Irish secular laws with the other countries of Europe.