In a statement sent to Aljazeera.net, Irish Labour Party spokesman on foreign affairs Micheal Higgins said Bigley's life should be spared as "no cause is advanced" from his execution.
"I am convinced that nothing at all will be achieved by the execution of Ken Bigley, whose aged mother is an Irish citizen," he said.
Bigley is entitled to carry an Irish passport himself and his family is hoping that this will increase his chances of release.
Ireland took a neutral position during the US-led war on Iraq.
Higgins slammed the Blair administration for not leaving any room for dialogue with Bigley's captors, who claim to be members of al-Tawhid and al-Jihad group.
"I and the Irish government are opposed to the Blair government's decision and by the appalling actions of the Bush administration," he told Aljazeera.net in a telephone interview.
"We must have dialogue with Iraqi groups, like the Association of Muslim Scholars. We are all interested in a peaceful resolution and putting an end to this illegal war," he said.
The captors have demanded the release of female Iraqi prisoners as a condition for Bigley's life to be spared.
"I find this hypocritical. We have peace in Ireland after negotiations and discussions and what we are seeing now is a double standard which reflects back to the Middle East peace process"
In a videotape released on Islamist websites on Wednesday, Bigley pleaded with Prime Minister Tony Blair to help him.
"This is possibly my last chance to speak to you," the presumed captive, whose voice breaks down several times in the footage, tells Blair.
"I need you [Blair] to be compassionate as you've always said you were ... I don't want to die ... Please, please release the female prisoners that are held in Iraqi prisons," he says, breaking down in tears.
"I need you to help me now, Mr Blair."
But earlier on Thursday, interim Iraqi Prime Minister Iyad Allawi blocked a previous decision by an Iraqi judge to release Iraqi biological weapons scientist Rihab Taha.
That decision dealt a huge blow to efforts to secure Bigley's safe release.
Bigley's brother, Paul, placed the blame on US President George Bush for wrecking possible chances for his release.
"A judge [in Iraq] has made a legal decision to release three people, one female and two males. The minister of justice has endorsed this [and] published this on international news.
"Now this has been sabotaged. I mean ... is this a puppet government, or are the Americans moving the goal posts to suit their own means again? What's going on here? Leave the Iraqis to do their own Iraqi business," he said in a radio interview.
Speaking to Aljazeera.net, the captive's brother said Bush was being "cocky and arrogant" and the Blair government was practising double standards by negotiating with the Irish Republican Army (IRA) and not with purported Iraqi groups.
Bigley made an emotional plea
to Blair on Wednesday
"I find this hypocritical," he said. We have peace in Ireland after negotiations and discussions and what we are seeing now is a double standard which reflects back to the Middle East peace process," he added.
Higgins agreed, calling the British and American decision not to negotiate "contradictory and appalling".
A spokesperson for the British Foreign Office said the UK government never negotiated with the IRA.
"To the best of my knowledge the government never negotiated with the IRA, they negotiated with Sinn Fein. But I'm not an expert," the official, who spoke on the condition of anonymity, said.
Higgins also emphasised his anger and frustration over the treatment of Iraqi detainees and scepticism about the stated number of Iraqi women prisoners.
"To say that there are only two women being held in Iraqi prisons ... I find that incredible, I simply don't believe it, I don't buy that," he said.
"To say that there are only two women being held in Iraqi prisons ... I find that incredible, I simply don't believe it, I don't buy that"
foreign affairs spokesman,
Irish Labour Party
"Especially when you consider the important role women play in Iraq and Islam and the cultural sensitivities of detaining women ... I find all of this outrageous. There should be an international team to look into how all prisoners are being held and I offer to be part of that team," Higgins added.
In other developments, a London-based Islamic organisation also urged the al-Qaida-linked group to free Bigley, saying he had been "let down" by his government.
"[Kenneth Bigley and his family] exhorted and begged the British government to rescue him from captivity but the British government's response was to shirk its moral responsibility," the Islamic Observatory said in its appeal to al-Tawhid and al-Jihad group.
"[Bigley] was let down by [Tony] Blair and his government, which is subservient to America," the statement read.