The GAA should be on a list of organisations of which Northern Ireland police officers must declare membership, a prominent Ulster Unionist has suggested.
UUP honorary secretary Ms Arlene Foster has opposed the register of organisations but said: "If a register is to be created and if the loyal orders are to be included from one side, then the GAA should be included from the other."
The Fermanagh and South Tyrone UUP representative said the register was "neither necessary nor proportionate", but insisted the GAA was a "quasi-political organisation" which opposed the British state.
Last week, the Police Service of Northern Ireland Assistant Chief Constable Sam Kinkaid announced officers would have to declare if they were members of organisations which could affect their jobs.
The PSNI listed several organisations including the Freemasons, the Orange Order, The Catholic Knights of Columbanus, the Royal Black Preceptory, the Ancient Order of Hibernians and the Apprentice Boys of Derry.
Nationalists criticised Ms Foster for saying the GAA should also be included on the list.
Mr Tommy Gallagher, of the SDLP, a former MLA for Fermanagh and South Tyrone, said a comparison could not be drawn between the association and the Orange Order.
"Unlike the Orange Order it does not bar membership to anyone on religious grounds," he argued.
"Gaelic games are encouraged and supported in all of our third-level institutions and indeed it is now played within the PSNI."
Mr Conor Murphy, a former Sinn Féin MLA for Newry and Armagh, said the comments showed "a large degree of ignorance about the role and the nature of the GAA".
But Ms Foster said: "The GAA was set up in the late 19th century in order to provide a focus for Gaelic nationalism in Ireland.
"Much has been made of the fact that the GAA has Protestant members and indeed has had Protestant presidents, but my reaction is, so what? That was not the point I was making, but then you can always trust the SDLP and Sinn Féin to bring sectarianism into the frame.
"The point I was making was that you would go a long way before you found a unionist who was a member of the GAA and the reason for that is that the GAA is anti the British state.
"The GAA is, despite what some would have you believe, a quasi-political organisation. Just as the Orange Order is quasi-political by wanting to maintain the British state, the GAA wishes to have a united Ireland.
"If it was not quasi-political, surely it would have no view on the constitutional issue and for that matter as an organisation it would not fly the flag of the Republic of Ireland at its matches in Northern Ireland."
She rejected the argument that the Orange Order was anti-Catholic. "I would advise the gentlemen who make those allegations to go and read the qualifications of an Orangeman," she said.
"Yes, the Orange Order is against the teachings of the Roman Catholic Church.
"But just take a look at what it says about the treatment of individual Roman Catholics. If there are allegations of ignorance flying around I think people in glass houses shouldn't throw stones." - (PA)