Proposals to introduce a form of "English votes for English laws" at Westminster risk creating second-class MPs in Northern Ireland, unionist and nationalist politicians have claimed.
The warning comes after Downing Street said ministers were looking "constructively" at the proposals of a commission set up to consider the balance of powers in the wake of devolution.
The McKay Report recommended in March that legislation that affects only England should normally need backing from a majority of English MPs, ending an "unsustainable" imbalance created by devolved administrations.
Reports suggest that English MPs will be given the power to veto any Westminster laws which do not relate to Scotland, Wales or Northern Ireland – such as those involving education, health and the environment – even if they have been passed by a majority of all MPs in the House of Commons.
The move, reportedly to be announced in the autumn, could restrict the ability of a future Labour administration to force through controversial legislation for England, as the party usually has a high proportion of MPs from Scottish and Welsh constituencies.
It would also have the potential to diminish the parliamentary leverage of the DUP's eight MPs, who form the fourth largest party in Westminster.
DUP MP Jeffrey Donaldson said: "We will obviously give it careful consideration but we remain of the view that it would be wrong to create two classes of MPs."
SDLP South Down representative Margaret Ritchie agreed that there was a danger of creating two tiers of unequal MPs.
"MPs are equal on election and remain so throughout the term. Giving a veto to English members would create two classes of MPs," she said.
Prime Minister David Cameron's official spokesman declined to say when the Government would respond to Sir William McKay's report.
In its response to Sir William McKay's commission, the SDLP said it had no desire to influence laws that only affect England. But it added: "A crude system of qualified and disqualified voting members within a democratically elected parliament could widen rather than narrow any perceived democratic deficit." The DUP wrote: "We view the Houses of Parliament and the monarchy as crucial unifying institutions... and creating some form of dual role for Parliament fundamentally undermines this." The Alliance said there would be a risk of creating "two classes of MPs".