Belfast City Council will send a second round of letters to the UK and Irish Governments asking to clarify the criteria for an Irish unity referendum.
It comes after Sinn Fein claimed both failed to answer the question directly.
In December the council sent a letter calling for the establishment of a New Ireland Forum alongside a series of Citizens' Assemblies ahead of a border poll.
The letter also called for specific details from both governments as to what conditions would facilitate a referendum.
Matthew Ellesmere, from the Northern Ireland Office in London, replied: "It remains the Secretary of State's view that a majority of the people of Northern Ireland continue to support Northern Ireland's place in the United Kingdom and that this is unlikely to change for at least the foreseeable future. The circumstances set out in the Belfast Agreement that require the Secretary of State to hold a referendum on Irish unification are therefore not satisfied."
Responses from both governments failed to mention specific criteria for a border poll.
At the recent full council meeting, Sinn Fein's Ciaran Beattie referred to the concluding sentence in the letter sent by the council last December: "The council agrees to write directly to the Taoiseach and to the British Secretary of State requesting that they clearly specify what would satisfy the requirement, as provided for under the terms of the Good Friday Agreement, to facilitate an Irish unity referendum."
Mr Beattie said neither government had answered the question in their responses, and the council should send another letter asking for "clarity".
DUP councillor David Brooks said the British and Irish Governments' responses should be noted, with no further action.
He said: "The idea that either government would form constitutional views or politics based on the view of this council is fanciful.
"One way we can cut down on motions here is by concentrating on those within the competency of this council - if we've said that once we've said it a thousand times."
Mr Brooks said there was no value in sending letters back and forward to the governments.
Alliance councillor Michael Long said: "I'd like to outline my environmental credentials and ask why we would waste a lot more paper on something where we wouldn't get a clear answer. I just don't see the point in sending another letter."
Mr Beattie in reply suggested the council could send an email.
The DUP amendment failed, with 17 members for and 25 against. The Sinn Fein proposal passed, and another letter will now be drafted and sent to London and Dublin.