But pro-choice activists want a more liberal regime, closer to that of England, which allows terminations to be carried out up to 24 weeks after conception. Opinion polls show a large majority of voters want some change.
Many at the march wore a black jumper with the word Repeal in white, a reference to a campaign to repeal the eighth amendment of the Irish constitution, which gives the unborn child equal rights to those of the mother.
A panel of citizens called together to advise government on the issue voted overwhelmingly that the eighth amendment should be changed.
An all-party committee in parliament is now considering those recommendations and is due to report to parliament by the end of the year.
Some of the crowd, who marched across the city before assembling outside the office of Prime Minister Leo Varadkar, chanted "Get your rosaries off our ovaries" in reference to the influence the Catholic Church has long had on social policy in Ireland, while others held posters demanding "Repeal now".
It was the sixth annual March for Choice organised by the Abortion Rights Campaign. Organisers estimated up to 40,000 attended.