The move will increase pressure on Taoiseach Enda Kenny who has defied calls to boycott the St Patrick's Day march in New York despite the decision of the city's mayor, Bill de Blasio, to boycott the event.
Boston mayor Martin J Walsh, who is the son of Irish immigrants from Galway, announced that he would not attend the event on March 16 unless organisers lift a ban on posters promoting LGBT rights.
Mr Kenny is scheduled to visit Boston on the day of the parade, however, he has not indicated whether he will march in the event.
Mr Walsh is the second US mayor to adopt such a stance after New York mayor Bill de Blasio vowed to boycott his city's parade.
Further pressure will now mount on Mr Kenny to change his mind.
Tanaiste Eamon Gilmore has backed Mr Kenny's decision to march in the New York procession but said he hopes the rules banning LGBT posters would change.
"The New York parade is a very important parade. I believe that the government should be represented at that parade, as it's always been," Mr Gilmore said.
"I think it's important that we are part of that parade. But I do believe that the rules of the parade should be changed and my views on that have been well known for some time."
Social Protection Minister Joan Burton has been criticised by her cabinet colleague Leo Varadkar after she vowed to boycott the same parade.
Ms Burton, who will be in New York on St Patrick's Day, called on organisers to make the event "more inclusive".
Mr Varadkar said that while he would like to see the rules surrounding posters changed, he believes such boycotts are counter-productive.
But Ms Burton's stance is receiving significant support from several Labour colleagues, with the party's Seanad leader Ivana Bacik accusing the parade organisers of discriminating against gay people.
"I fully support Minister Joan Burton in her welcome decision not to participate in an event that sends a message of exclusion and intolerance towards a whole community," Ms Bacik said.
"The discriminatory stance of the parade organisers is out of keeping with a modern and progressive Irish identity that seeks to embrace diversity. I would urge other Irish ministers and political leaders to follow the principled stand taken by Minister Burton and (New York) Mayor De Blasio."