Alliance has expressed disappointment a bid to declare Brexit as not an "orange or green" issue and reflect its impact on all in Northern Ireland was rejected by Belfast councillors.
During the monthly meeting of Belfast City Council on Monday night, Sinn Fein tabled a motion calling for the British and Irish governments to state the specific requirements for a border poll to be called.
Under the terms of the Good Friday Agreement, the Secretary of State for Northern Ireland must call such a poll if it is likely a majority would vote in its favour.
Sinn Fein's motion was framed around Brexit, stating that it is a "damaging policy of attempting to drag citizens out of the European Union against the wishes of the majority of citizens in Belfast who voted to remain".
The motion stated, "this council must, therefore, investigate alternative solutions to Brexit that seek to protect its citizens from the damaging effects which Brexit will ultimately bring" - such as an Irish unity referendum.
"We call upon this council 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," it concluded.
Alliance council group leader Michael Long attempted to bring an amendment to the motion stating: "Brexit is not an orange or green issue and attempts to make it so are profoundly unhelpful" and the council will investigate the Belfast-related issues around Brexit through the council's Brexit committee.
Sinn Fein, the SDLP and People Before Profit voted against hearing the amendment, so it was defeated.
Speaking following the meeting, Mr Long said Brexit will affect everyone in Northern Ireland equally, "whether unionist, nationalist or other".
“That’s why Alliance attempted to bring this amendment. We recognise there is a fluid debate on the future of Northern Ireland and the desire for Irish unity is a perfectly legitimate position but we are clear whatever the constitutional position, the priorities must be to promote reconciliation, make this region work and fight against the devastation Brexit will bring," he said.
“Given the SDLP’s talk of how important it is to promote Remain during this election, it was particularly disappointing they voted against this amendment, meaning when push came to shove, they prioritised Irish unity over a combined, non-political approach to tackling Brexit.”
Sinn Fein's original motion was passed, with 27 votes in favour and 22 against.
The SDLP has been contacted for a response.