Prime Minister Theresa May has said it is not the right the time for Ireland to hold a border poll on unification.
Mrs May said parties in Northern Ireland should instead be focused on reforming the Executive after the collapse of power-sharing.
DUP MP Nigel Dodds accused Sinn Fein of causing further “uncertainty and division” by its fresh calls for a border poll on Irish unity.
Speaking as she delivered a statement to Parliament on last week’s European Council meeting, Mrs May said: “There are a set of circumstances which the secretary of state for Northern Ireland has looked at this issue, and it is not right to have a border poll at this stage.
“What we should all be focusing on is bringing the parties together to ensure that we can continue to see the devolved administration in Northern Ireland working, as it has done, in the interests of the people of Northern Ireland.
“We want to see that devolved administration being formed and that’s what all the parties should be looking for at the moment.”
Sinn Fein has said there is an urgent need for a referendum on Irish unity as the British government has “refused to listen” to the majority of people in Northern Ireland over Brexit.
Belfast North MP Nigel Dodds said: “Following the successful conclusion of the Article 50 Bill last night, there are some in Northern Ireland who would add to the uncertainty and division by calling for a border poll.
“They’ve already created enough uncertainty and division by collapsing the institutions in Northern Ireland.”
Addressing the prime minister, he added: “Would she take this opportunity to tell people that there’s never been more support for the Union in Northern Ireland across all communities, and that in fact such a call is outside the terms of the Belfast Agreement – the very point that Sinn Fein keep harping on about, that they want the implementation of the agreements.”
Meanwhile, Lady Hermon, the independent MP for North Down, urged the prime minister to personally intervene in Northern Ireland to “turn back the tide” of support for Sinn Fein.
She said: “Fears over the consequences of Brexit have undoubtedly been exploited by Sinn Fein in the recent Northern Ireland Assembly election.
“Sinn Fein increased its first preference vote by somewhere in the region of 58,000 first preference votes.
“That means that Sinn Fein is just one seat behind the Democratic Unionist Party in the new Assembly as elected.
“I wonder, and I’m sure the country wonders and particularly those in Northern Ireland, what steps the prime minister is going to take, including visiting Northern Ireland, to turn back the tide of support for Sinn Fein?”
Mrs May said the focus in the coming weeks must be on bringing the parties together to form a new devolved administration.
She added: “We have been very clear about the relationship that we want to ensure in relation to the border with the Republic of Ireland and we continue to work with the Republic of Ireland and others on delivering on that.”
Meanwhile, she also told MPs that Brexit should not be described as a “divorce”, because it suggests the UK and European Union will be on bad terms after they split.
The issue was raised during the prime minister’s statement on her recent trip to the European Council by Labour’s Angela Smith.
The MP for Penistone and Stocksbridge said: “There’s been a lot of emphasis on the trade deal but the divorce deal is very important too and at the heart of any divorce deal is a fair financial settlement.
“What will the prime minister do if there is no fair financial settlement at the end of the Article 50 period?”
Mrs May replied: “You will be aware as we enter the negotiation there is a wide range of issues that we will be looking at and discussing with the European Union.
“But I didn’t raise this earlier ... but a number of people have used this term of divorce.
“Actually, I prefer not to use a term of divorce from the European Union because very often when people get divorced they don’t have a very good relationship afterwards.
“Honourable members need to stop looking at this as simply coming out of the European Union and see the opportunity for building a new relationship with the European Union and that’s what we will be doing.”