THE SDLP and Alliance backed a pan-unionist proposal to erect a stone monument at Stormont to mark the centenary of Northern Ireland.
The DUP, UUP and TUV submitted a proposal to the Assembly Commission to permanently mark the date within the "curtilage of Parliament Buildings".
However, they claim Sinn Féin has "vetoed" the plan.
Sinn Féin said the proposal should first have been discussed with other parties and the monument – in the shape of Ireland's six north-eastern counties – "reflects only one political perspective".
A joint statement from the unionist parties' leaders said they were "dismayed" that the Assembly Commission had not given the go-ahead to the monument, which would be paid for from party funds and MLAs.
"This is the party that talks most about respect for all communities, but when a modest proposal was made on behalf of the wider unionist community it was callously vetoed," the statement from DUP leader Arlene Foster, UUP leader Steve Aiken and TUV leader Jim Allister said.
Sinn Féin said the "centenary of partition" could offer an opportunity to "embrace the very different perspectives of that event".
"Unfortunately, the proposed stone has been designed and commissioned by representatives of one tradition and reflects only one political perspective," it said.
The SDLP said its support came "in a spirit of generosity".
“As the late John Hume said, difference is the essence of humanity – the answer to difference is to respect it."
It added: “The SDLP believes that there should be a broader review of monuments within the Stormont Estate and Parliament Buildings to reflect the diversity of our society.”
Alliance said the party regarded the monument as a "modest plan to commemorate a significant event".
"The stone was intended for the Stormont Estate and was only one component of an overall series of proposals to mark the centenary of Northern Ireland this year.
“While we respect everyone has a different view on partition, the centenary should be marked in a shared, inclusive way, with a focus on the future.”
