DUP leader Sir Jeffrey Donaldson insisted he had taken the decision to send a ‘clear message’ to the EU and the UK government on resolving issues with the Northern Ireland Protocol .
But Ms O’Neill accused the Unionist party of ‘punishing the electorate’ while Alliance party leader Naomi Long said it had been a ‘shameful day’ for the DUP.
Failure to elect a President prevents the Stormont Assembly from functioning.
The DUP is also refusing to nominate for the post of Deputy Prime Minister, which prevents the formation of a new executive, as part of its protest against the protocol.
The 90 MPs gathered for the first time in Stormont Chamber on Friday after Northern Ireland Assembly elections last week saw Sinn Fein become the largest party for the first time.
The first thing to do was for the deputies to sign the list of members before attempting to elect a president.
Unionists oppose the post-Brexit treaty because of the economic barriers it creates between Northern Ireland and the rest of the UK.
Outlining his reasons for blocking the election, Sir Jeffrey said: “As I made clear this morning, we have made the decision not to support the election of a President at this stage.
“I think we need to send a very clear message to the European Union and to our government that we are serious about resolving this protocol.
“Because of the harm it is causing, undermining political stability, damaging the agreements which have formed the basis of political progress in Northern Ireland, to our economy, contributing to the cost of living crisis, this issue must be addressed. processed.
“While others sit idly by, we are not ready to do this. We need decisive action from the government.
He added: “The choice is clear: if the European Union is serious about protecting political institutions and the Belfast Agreement, and its successor agreements, then it knows what to do.
“Similarly, the same message is also there for our own government. The ball is firmly in the hands of the government.
Sinn Fein leader Stormont, Ms O’Neill, responded by saying that the DUP had “punished the electorate” by boycotting the election of a Speaker of the Northern Ireland Assembly, and that “the public deserves better”.
She added that the DUP’s action to boycott the election of a Speaker of the Assembly “is not tolerable, is not acceptable, is not good enough”.
Ms O’Neill has confirmed that the Prime Minister will visit Northern Ireland on Monday.
Alliance party leader Ms Long said: ‘Although this is a sad day for the people of Northern Ireland, it is a shameful day for the DUP.’
As the largest party, Sinn Fein’s 27 MPs took their positions on the benches on the right side of the Speaker’s chair for the first time.
He has the right to appoint his Stormont leader Michelle O’Neill as first minister, but she will not be able to take on the role without the DUP appointing a deputy first minister.
According to the rules of decentralized administration of power sharing, the two roles are equal and one cannot be in office without the other.
Since last week’s election, Ms O’Neill has repeatedly called on the DUP to reinstate the executive so it can begin to tackle challenges such as the cost-of-living crisis and spiraling job slates. waiting for hospitals.
The Stormont session comes amid heightened tensions between the Westminster government and the EU over the operation of the protocol, which is part of Britain’s Brexit deal.
It comes after Foreign Secretary Liz Truss said the UK would have ‘no choice but to act’ if the EU did not show enough ‘flexibility’ on post-checks. Brexit on goods going from Great Britain to Northern Ireland.