The incoming Prime Minister Rishi Sunak must deal with Brexit's Northern Ireland Protocol "once and for all" if he wants Stormont restored, the DUP leader has said.
Sir Jeffrey Donaldson said while the new Conservative leader may be focused on uniting his party after weeks of turmoil, "the unity of our United Kingdom must be protected".
Alliance leader Naomi Long also reacted to Mr Sunak becoming the next Prime Minister, urging the former Chancellor to reform the devolved institutions to bring an end to "ransom politics".
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Stormont has been in limbo with the DUP blocking the restoration of power-sharing in protest over the protocol, which has created trade barriers between Great Britain and Northern Ireland.
The UK Government has vowed to secure changes to the protocol, either through a negotiated compromise with the European Union or domestic legislation to override the arrangements.
If the Stormont institutions are not restored by Friday, the Secretary of State is required under legislation to call an early Assembly election.
In his message to the new Prime Minister, Sir Jeffrey said: "There may be a focus on the unity of the Conservative Party, but the unity of our United Kingdom must be protected.
"The protocol is incompatible with the restoration of devolved government in Northern Ireland.
"If the Prime Minister wants to see a fully functioning Stormont, then he must deal with it once and for all.
"Delivering that solution would be a very powerful signal that he is focused on building a better future for everyone."
Mrs Long urged Mr Sunak to take a "fresh approach" to political problems in Northern Ireland.
She said: "Northern Ireland needs stable and sustainable government.
"Rishi Sunak needs to recognise, even if a solution to the protocol can be agreed with the EU, there remains an inherent instability at the heart of our institutions.
"The protocol is only the latest in a long line of grievances to have collapsed Stormont.
"Until the institutions are reformed to remove the vetoes the largest parties wield over Executive formation, the crisis-collapse cycle will continue."
Sinn Fein president Mary Lou McDonald said a protocol deal between the UK and EU could be done "very quickly" and the challenge for the next Prime Minister was ensure people were “not left endlessly in a limbo”.
Speaking in Belfast ahead of Mr Sunak being confirmed as the next Prime Minister, she accused the DUP of "gross political negligence".
She said: "The DUP claim to be committed devolutionists, yet all they have done is left us at the mercy of the dysfunction at Westminster and the chaotic Tory party."
SDLP leader Colum Eastwood said the process of appointing Mr Sunak as Prime Minister was a "farce" and called for a general election.
The Foyle MP added: "Mr Sunak's predecessors have completely destroyed the public's confidence in politics and public service and wrecked the economy and he should not be allowed another two years to desperately attempt to clean up their mess.
"The circus that has surrounded British politics has to end and the only way to do that is through a general election and the establishment of a Labour-led government."
Ulster Unionist leader Doug Beattie said the UK was desperate for a strong and stable government.
He added: "Northern Ireland needs better government and that means the restoration of the devolved institutions.
"One of the new prime minister’s priorities must be resolving the political impasse and dealing with the issues caused by the Northern Ireland Protocol.
"Northern Ireland cannot continue to be used as political football between the United Kingdom and the EU. The protocol must be replaced with a deal that works for everyone."
Meanwhile, the chief executive of the Northern Ireland Chamber of Commerce and Industry said she hoped Mr Sunak’s victory would lead to "economic stability and political certainty".
Ann McGregor said: "Given the significant fiscal pressures we face and with only days left until Northern Ireland could find itself without devolved ministers, we would urge the new prime minister and the UK Government to do all that they can, without delay, to work with local parties to restore a fully functioning Executive."
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