His rank and full name were read into the record by Meath West TD Peadar Tóibín, the leader of the one-seat Aontú party.
Soldier F had been facing prosecution in connection with the Bloody Sunday events of 50 years ago in which 13 civilians were murdered, with a 14th victim dying shortly afterwards, but last year it was announced that the prosecution would not be going ahead.
But the British government is proposing an amnesty in relation to Troubles-related crimes of the last century.
Mr Tóibín said he was naming soldier F because such identities should be in the public domain, “so people know what they have been doing throughout the country.”
He was also referring to a new Northern Ireland ombudsman’s report into “collusive behaviour” between the RUC police force and Loyalist paramilitaries from 1990 to 1998 that led to eleven murders and one attempted murder.
The Ceann Comhairle did not intervene after the naming of Soldier F and the Taoiseach showed no reaction to the alleged identification itself.
Instead Mr Martin said: “In respect of his claims, it is the case that heinous crimes were committed against many people.”
He told Deputy Tóibín: “You’re correct in saying that people want closure. They want details. They want to find out what happened their loved ones and who killed their loved ones.”
He said the Irish Government has entered into discussions with London and all parties in Northern Ireland over the proposed amnesty “that emanated from the British Government last year,” he said.
“We've made it very clear that we do not accept any unilateral actions in respect of legacy issues. That would represent a breach of the Good Friday Agreement and subsequent agreements.
“The proposals cannot be accepted. We've opposed them, and we made it very clear to the British Government that there can be an amnesty for nobody.”
State forces and Governments should have “a higher moral order in terms of how they conduct themselves,” the Taoiseach said, but no paramilitaries should have an amnesty either, he said.
Mr Tóibín said: “If there is an Amnesty it means there is no rule of law. If there is an amnesty the perpetrators will get away with murder.
“Over the last few debates in the Dáil I have named the victims of the Blood Sunday Massacre, the Bally Murphy Massacre, the Spring Hill Massacre, the murders researched in Operation Greenwich and today those discussed in the latest Ombudsman report.
“It’s shocking that we have the names of those who have been murdered, yet people don’t know the names of the people who killed them. The perpetrators names remain invisible.
“Most people don’t know the name of (Rank and Name), better known as Soldier F, accused of murdering five people on Bloody Sunday. Most people don’t know the names of the other alphabet of British Soldiers who have murdered civilians.
“Taoiseach what will you do to change that?”