Northern Ireland Secretary James Brokenshire has said special status for Northern Ireland after Brexit would be the wrong approach, amid fears such a deal could undermine its place in the United Kingdom.
DUP MP Sammy Wilson (East Antrim) said there should be no special circumstances "that will weaken our position within the United Kingdom" when Britain leaves the EU.
Mr Brokenshire agreed, saying that special status would be "the wrong approach".
He added that the Government intended instead to look at addressing individual issues specific to Northern Ireland during Brexit negotiations.
This week Sinn Fein launched a campaign in a bid to secure special status for Northern Ireland within the EU after Brexit.
Speaking at Northern Ireland questions in the Commons, Mr Brokenshire also renewed his pledge to maintain a "frictionless" border between Northern Ireland and the Republic of Ireland.
But he was accused of giving vague answers on the details of such an arrangement, as MPs pressed him on the relationship between the two countries after Britain leaves the EU.
Mr Wilson said: "The Government has rightly sought to identify the issues that affect different regions and different sectors of the economy, and to build those into its negotiating position.
"Regardless of the issue, however, of the common travel area, can the Secretary of State give us an assurance that all parts of the United Kingdom will leave the EU on an equal basis, and that no special arrangements or different conditions or special circumstances will be afforded to Northern Ireland, that will weaken our position within the United Kingdom, and treat us differently than other parts of the United Kingdom?"
Mr Brokenshire replied: "We are very clear as a Government of the strength of the union, how that matters to all of us.
"Therefore the approach that we take is based on getting the best possible deal for all parts of the United Kingdom.
"Yes, there will be some specific factors in Northern Ireland, that he is well aware of. We've talked about the border, and there are other issues as well.
"But it is with that intent, it is with that focus, and therefore concepts of special status I think is the wrong approach.
"It's rather looking at special factors, special circumstances, and dealing with them effectively."
The SDLP's Alasdair McDonnell said there was "a gap between the wishful thinking and the reality of movement of goods" when it comes to the common travel area, if Britain leaves the customs union.
SNP MPs also pressed Mr Brokenshire on how the border arrangements would stop EU citizens moving between the Republic of Ireland and Northern Ireland.
Mr Brokenshire said: "She (Theresa May) underlined that clear desire that we have as a Government in the negotiations ahead to get the best possible trading arrangements with the European Union, and therefore we are reflective as to how we do that, whether that is some form of membership of a customs union, or a bespoke customs arrangement.
"But he should be very intent on our desire to get that deal, and also to see a frictionless border between Northern Ireland and the Republic of Ireland."
Labour's Jeff Smith (Manchester Withington) said leaving the EU would affect Northern Ireland more than any other region of the UK, given the amount it exports to the bloc.
He added: "The previous answer was pretty vague, so what specific steps will the Secretary of State take to ensure that those exports are protected, in order to protect inward investment?"