The legal action is being brought by three Irish women who say the effective ban on abortion in Ireland violates the European Convention on Human Rights.
All three have travelled to Britain to have abortions.
The Irish government has engaged two leading lawyers to argue its case that the country has a sovereign right to protect the life of the unborn.
The three Irish women will be identified only as A, B, and C during the Strasbourg court hearings.
They argue that being forced to travel abroad for abortions endangered their "health and well-being" as safeguarded by the European Convention on Human Rights.
The two constitutional lawyers representing the government of Ireland argue that the convention's safeguards cannot be interpreted as endorsing the right to abortion.
The case is the first challenge to Ireland's abortion laws in more than 15 years, the BBC's Europe correspondent Jonny Dymond says.
Almost 140,000 Irish women have travelled to Britain over the past 30 years to have abortions, our correspondent adds.