The motion was defeated by 42 votes to 32 at the IMO's annual conference.
The AGM has also rejected abortion in the case of victims of rape or incest who become pregnant.
Doctors also rejected a call for legislation for abortion in the case of a woman with a non-viable foetal abnormality.
Debate on the abortion motions lasted 100 minutes.
She said women's lives were being compromised under the current position.
Dublin GP Dr Cyril Daly said he was reminded of German doctors during the war, who conducted tests and carried out abortion, and he asked the IMO to resist the pressure to import abortion into Ireland.
A row broke out over the limited time to debate the issue, with calls for the suspension of the standing order and shouting from the floor at the top table.
Dr Eleanor Corcoran, a psychiatrist, said if the motion was passed it would mean abortion on demand.
Non-consultant hospital doctor Mark Murphy said the motion just reflected what was the law.