SECRETARY of State Theresa Villiers last night dismissed the prospect of a border poll, saying political attention was "better focused elsewhere".
DUP enterprise, trade and investment minister Arlene Foster had earlier said her party might "call Sinn Fein's bluff" over calls for a referendum on Irish unification.
The surprise response came after Sinn Fein president Gerry Adams launched his party's campaign for the first border poll in almost 40 years.
He put economic arguments to the fore, arguing that unification would bring greater prosperity.
The Good Friday Agreement allows for a referendum to change Northern Ireland's constitutional status, though the decision rests with the secretary of state.
It states that he or she shall exercise the power "if at any time it appears likely... that a majority of those voting would express a wish that Northern Ireland should cease to be part of the United Kingdom and form part of a united Ireland".
It adds: "The secretary of state shall not [make this order] earlier than seven years after the holding of a previous poll."
Mrs Foster said the economics of a united Ireland did not make sense.
"Northern Ireland currently receives a £10 billion subvention from the treasury - there has never been a rational argument put forward as to how this gap would be filled," she said.
"Whilst Sinn Fein talks about a border poll it is the last thing they would want as they know the outcome would be so resounding - they should be careful what they wish for."
The Fermanagh and South Tyrone MLA said her party could "put an end to this foolish talk once and for all".
"The DUP is having this discussion but has not reached a conclusion on the matter," she said.
Sinn Fein's general secretary, Mitchel McLaughlin, described a border poll as one of the "outstanding issues" within the Good Friday Agreement.
"For too long the negative impact of partition has seen the economic strength and potential of the island of Ireland muted and arrested - this continues today," the South Antrim MLA said.
"Further to this the recent census has shown that there is a new outlook in regards to identity within the north of Ireland."
Former UUP leader Tom Elliott described calls for a poll as a "divisive, political stunt".
"The Ulster Unionist Party has nothing to fear from a border poll but Sinn Fein should move on and stop wasting time and money," he said.
Yesterday's exchanges appeared to be in vain as Ms Villiers stepped in last night.
She said: "Given the state of opinion in Northern Ireland, which is clearly expressed in election results and opinion polls, the government has no present plans to call such a poll.
"It is crucial that political leaders here concentrate on working together on pressing economic and social issues, including the rebalancing of the Northern Ireland economy and building a genuinely shared society, rather than being diverted into divisive constitutional debates."
■ CALL: Sinn Fein president Gerry Adams delivers a keynote speech at the Regency Hotel in Dublin yesterday. He called on the British and Irish governments to set a date for a referendum on the unification of Ireland