Michael D Higgins will ask the Council of State if the Protection of Life During Pregnancy Bill's legality should be tested by the Supreme Court.
The bill would allow a termination when doctors deem that a woman is at risk of taking her life.
President Higgins must decide by Wednesday whether to sign the bill into law or refer it to the court.
If the Supreme Court decides it is constitutional and approves the bill, it will automatically become law and its constitutionality could never be subsequently challenged.
It the first time that President Higgins has convened the Council of State since he assumed office in November 2011. The Council of State is an advisory body that aids and counsels the president.
The introduction of the legislation follows the case of an Indian woman who died in an Irish hospital after she was refused an abortion.
The debate revealed deep splits in the predominantly Catholic country.
Anti-abortion campaigners say that the bill will allow the intentional killing of the unborn for the first time in the Republic of Ireland.
Others argue the bill is too limited as it does not allow for terminations in cases of rape or incest, or when there is a foetal abnormality or when the foetus cannot survive outside the womb.
Since a Supreme Court ruling in the 1992 X case, abortion has been constitutionally available when a woman's life, as distinct from her health, is at risk from the continued pregnancy.
X was a suicidal 14-year-old schoolgirl who had been raped by a neighbour and was initially prevented from leaving the country for an abortion in Britain.
Since then, the credible threat of suicide is, constitutionally, regarded as grounds for a termination.
But until now, no government in the republic has introduced legislation to give doctors legal certainty on when an abortion can be carried out.
That uncertainty provided part of the context for the Savita Halappanavar case.
She was a 31-year-old Indian dentist who was admitted to hospital in Galway in October 2012 while miscarrying.
She died a week later from septicaemia.
Her request for an abortion was turned down.
Her inquest heard that she could not get a termination at the time because her life was not in danger but, by the time her life was at risk, an abortion would have been too late to save her.
A bill giving limited access to abortion has been referred to an advisory body by Ireland's president.