The Government has voted down a People Before Profit motion to have a referendum in order to insert Ireland's neutral status into the Constitution.
The vote was 53 in favour with 67 against.
The PBP TD Paul Murphy said the outcome was a "shame".
He accused the Green Party of "supporting the militarists" in Fianna Fáil and Fine Gael.
Earlier today, the Dáil heard that the Irish Republic is under attack from those - including the Government - who want to undermine its neutrality.
Solidarity-People Before Profit warned that the Ukraine crisis is being used to push such "militarisation" as it sought a motion to have a referendum on Ireland's neutrality status.
The party's TD for Dún Laoghaire Richard Boyd Barrett said many people believe that neutrality already has such a guarantee [in the Constitution], as it has such "long-standing and overwhelming" support.
He also accused the Government of being "dishonest and misleading" in its opposition to the bill.
"Ireland's neutrality and the struggle for an independent Irish Republic are one and the same thing", he said, and warned that moves against neutrality amount to "a betrayal of the Republic".
Neutrality has been "seriously under attack" from successive governments who have sought to undermine it, Mr Boyd Barrett said.
Most grievously, this occurred when Ireland allowed US troops to use Shannon while executing "bloody and unjustifiable wars in Afghanistan and then Iraq," he said.
He also accused successive Irish governments of facilitating the "outrageous practice of rendition", which was simply "kidnapping and torture", conducted with the cooperation of "brutal and despotic" regimes.
With Russia's invasion of Ukraine, Mr Boyd Barrett said that the Government is seeking "to exploit that terrible crisis in order to move towards greater EU militarisation... and closer alignment with NATO".
Party colleague Bríd Smith appealed to the Green Party to vote "according to their consciences", and refuse to oppose the bill, which the Government has said it will do.
She pointed to the "spectacular hypocrisy" in Ireland's response to refugees from Ukraine, compared to those from Yemen or Afghanistan.
"We serve neither Putin nor NATO, nor any other imperial bloc", Ms Smith said.
"You intend to march us to war in future alliances" without the option of a referendum, she told the Minister for Foreign Affairs, Simon Coveney.
But Mr Coveney insisted that neutrality has never stopped Ireland from "participating in world events".
He quoted JFK, who told the Dáil in 1963 that Ireland "is not neutral between liberty and tyranny". He pointed to Ireland's aid to Ukraine being used "only for non-lethal equipment and support".
Mr Coveney warned that the bill could constrain the Government's ability to take part in peace-keeping missions, particularly UN missions "with a peace-enforcement (or Chapter 7) mandate".
It could "neutralise the ability of the Irish Defence Forces to operate overseas", he said, and even "prevent the provision of non-lethal equipment", including to Ukraine, through the European Peace Facility.
"To be blunt, it could prevent us from putting our money where our mouth was," Mr Coveney cautioned.
Sinn Féin supported the bill, with Foreign Affairs Spokesperson John Brady agreeing that some are trying to use the crisis in Ukraine to abandon Irish neutrality in favour of "jingoism".
Labour's Brendan Howlin expressed reservations about its wording, but welcomed the bill in the hope that it will prompt a wider debate on Ireland's neutrality.
