The secretary of state has ruled out the possibility of Northern Ireland having special status after Brexit.
Speaking in the House of Commons, James Brokenshire said applying special status was the "wrong approach".
The government is working to get a deal after Brexit that is best for all parts of the UK, he said.
Mr Brokenshire was responding to a question from DUP MP Sammy Wilson, who said that "all parts of the UK should leave the EU on an equal basis".
MPs have been debating a bill that would give PM Theresa May the power to begin negotiations over withdrawal.
The bill, if passed, will allow the prime minister to trigger Article 50 of the Lisbon Treaty by her own deadline of 31 March.
Sinn Féin and the SDLP have both called for Northern Ireland to have special status after the UK leaves the EU.
But Mr Wilson, whose party campaigned for Brexit, said the DUP wanted to see the process of leaving commence as soon as possible, adding that it would oppose attempts of "parliamentary guerrilla warfare" to block the government's plans.
He told the BBC it was "an historic day for the UK".
"The promise, which was made when the referendum was granted, giving the people of the UK the final say on EU membership, must be honoured," he said.
The SDLP has joined forces with the SNP at Westminster and backed an amendment.
It states: "The government has failed to properly consult with the devolved administrations and has, so far, failed to produce a white paper on its plan for Brexit."
SDLP MP for South Down Margaret Ritchie said: "Brexit will be damaging to our economy and society.
"British and Irish governments working with the Northern Ireland Executive need to secure special status, which involves continued access and membership of the Single Market and Customs Union to protect and safeguard our economy and communities."
The Ulster Unionists, who campaigned to remain in the EU, are to back the move to trigger Article 50.
Its South Antrim MP, Danny Kinahan, said: "We need the whole Leave process to start so we can lessen uncertainty and start tackling all the issues.
"We need clarity as there is so much to cover, affecting everyday lives."
Sinn Féin believes Northern Ireland should have special status within the EU.
Its leader north of the border, Michelle O'Neill, said: "Brexit is not just an issue for the north. It will be a disaster for our economy north and south."
Independent MP Lady Sylvia Hermon said she will vote against the bill: "A clear majority of people in Northern Ireland voted for the UK to remain in the EU and a majority in my North Down constituency voted in favour of remain," she said.
"I voted to remain as I do not believe Brexit will be good for the country. I haven't changed my mind."
The bill being debated at Westminster was published last week, after the Supreme Court decided MPs and peers must have a say before Article 50 could be triggered.
MPS are due to vote on Wednesday night.