DUP leader Arlene Foster has said "extending deadlines does nothing to encourage a deal", as Prime Minister Theresa May announced the possibility of delaying Brexit.
In a statement to the Commons on Tuesday, Mrs May said she will put her Withdrawal Agreement to a "meaningful vote" by March 12. If that fails, MPs will be offered two separate votes in the following days.
One will be on whether MPs support a no-deal Brexit and the other will be requesting an extension to the two-year Article 50 negotiation process beyond March 29.
Following a meeting with Mrs May, Arlene Foster urged the Prime Minister to deliver on her commitments to seek changes to the Withdrawal Agreement.
"We support a sensible deal and a managed exit from the European Union. Parliament has mandated the Prime Minister to seek a replacement of the backstop," she said.
"At that time, the Prime Minister committed to seek legally binding changes to the Withdrawal Agreement.
"This position commanded a clear majority in Parliament. Mrs May should deliver on those commitments. Experience in Northern Ireland has shown that extending deadlines does nothing to encourage a deal.
"A no-deal outcome can be avoided and it can be agreed long before the March 29. The European Union have it in their hands to avoid such an outcome. They know exactly what is required to achieve a deal which Parliament can support.
"It's time for Dublin and Brussels to be in a deal-making mode."
Ulster Unionist leader Robin Swann said a Brexit delay will be worth it if it results in a better deal.
"If (a delay) ensures we get a deal, then a short extension is unfortunate but worth it in the end," he said.
"We want to see the referendum result honoured but, with a deal for Northern Ireland that does not include the backstop which undermines the Belfast Agreement and the principle of consent.
"The Brexit which the DUP promised will not be delivered by the present proposals."
In response to Theresa May's statement, Labour leader Jeremy Corbyn said his party will put an alternative Brexit plan before MPs on Wednesday.
He said the plan is based around a "new customs union with the EU" and "close alignment" with the single market.
"The Prime Minister's botched deal provides no certainty or guarantees for the future and was comprehensively rejected by this House," he added.
"If it somehow does pass in some form at a later stage, we believe there must be a confirmatory public vote to see if people feel that's what they voted for."