The motion, describing the introduction of legislation as "fair and proper treatment for the Irish language community", received the backing of the majority of councillors at a full meeting of Belfast City Council last night.
It was supported by 34 councillors, with 22 voting against, after a debate lasting almost an hour.Matt Collins, from People Before Profit, introduced the motion and it was seconded by the SDLP's Dónal Lyons.
At the start of the meeting, councillors heard from Ciarán Mac Giolla Bhéin from Conradh na Gaeilge, who said that "Irish belongs to nobody but it is owned by everybody".
"Our campaign will only intensify. An Irish Language Act was promised by the St Andrew's Agreement. This is not the 16th century, this is 2018," he said.
Opening the debate, Matt Collins said: "It is the DUP that has politicised the Irish language over the last two years or so. They want to use it to deflect from their own right wing policies."
Sinn Féin's Séanna Walsh pointed out that "there is an Irish inscription on the mayoral chain" and noted that "the sky didn't fall in" when unionist mayors wore it.
"People have got to wise up in relation to this issue," he said.
However, unionists of all shades spoke to oppose the motion.
Deputy Lord Mayor and UUP councillor Sonia Copeland said that the "real issue here is mutual respect" and, referring to the Irish Language Act, added that the chamber could not vote on something it "doesn't know the contents of".
Her party colleague Chris McGimpsey outlined that he was opposed to an Act, but spoke of his own involvement with the Irish language and said he was "personally appalled" by the decision of the DUP's Paul Givan to remove a £50,000 bursary for Gaeltacht pupils in December 2016.
The DUP's Lee Reynolds dismissed claims there was no politics involved in the campaign, citing the Gaelic revival period and research which "showed that one of the reasons given for learning Irish in west Belfast was Bobby Sands".
"Now tell me that isn't political," he said, describing Conradh na Gaeilge's proposal for an Irish Language Act as "Swiss cheese".
Michael Long of Alliance said that while he believed it "is not the most important issue", it was clear power-sharing would not return without a resolution to the question.
Meanwhile, a planned motion calling for the council to back the decriminalisation of abortion has been postponed.
The motion states: "A woman who has an abortion is not a criminal, nor are healthcare professionals who care for them, and the law should not treat them as such."
Kate Nicholl, the Alliance councillor who had tabled the motion, was unable to attend the meeting and it was agreed to defer the de