That position will bring together all 13 Northern Ireland MPs who take their seats in the Commons.
Sinn Fein is meanwhile pressing for a “common approach”, even though its five MPs boycott Parliament.
David Cameron sparked fears of a cutbacks agenda during the election campaign, when he singled out Northern Ireland as a region where the state is “too big”.
He strongly denied claims that the province would be targeted, saying he wanted to rebalance the economy over a long-term period. His supporters also stated that spending cutbacks across the UK were inevitable, whoever won the General Election.
In a statement last night, Sinn Fein deputy First Minister Martin McGuinness said some local MPs had been “trying to exaggerate their influence” in the hung Parliament situation.
He also said: “Developing a common approach to secure the best block grant possible and to resist cuts to public services will be a priority issue in the days ahead. Indeed it is my view that the Executive should discuss this matter urgently.”
Mr McGuinness added: “We need to be ready and united to stand up to a Tory/Lib Dem coalition who will want to press through cuts to frontline services.”
DUP MP and Stormont Finance Minister Sammy Wilson said: “Whilst Northern Ireland has specific needs after suffering for so long from terrorism, and unique circumstances with a land frontier bordering the Republic of Ireland, the DUP has always said we would work with any of the main parties to secure a good deal for Northern Ireland and in the overall national interest. DUP MPs will continue to highlight the needs of Northern Ireland with the newly formed Government.
“We will be stressing our opposition to some proposals which emerged for quick and deep cuts to our public services which would damage our chances for economic recovery.”
SDLP leader Margaret Ritchie vowed to fight “Tory cuts” and said she would be seeking a meeting with the new Prime Minister and incoming Secretary of State for Northern Ireland as soon as possible.
“We have a responsibility to the people who elected us to ensure that we continue to challenge the British Government to get the best deal for all the people of Northern Ireland,” she said.
“All parties have a duty to maximise the regional interest here in Northern Ireland, such as protecting the block grant and our public services — especially in terms of the cuts David Cameron seemed to be talking about during the election campaign.”
New Alliance MP Naomi Long said: “We need stable Government if we are to deal with the economic crisis facing the UK and create the conditions where Northern Ireland can grow its private sector and maintain high quality public services.
“We want to see a united group of Northern Ireland MPs working together to safeguard the block grant, prevent unfair cuts and see that priority issues are addressed.”