Sinn Féin's leader at Stormont has accused the DUP of holding the public to ransom and denying democracy by refusing to elect a Speaker at Stormont or form an Executive in Northern Ireland.
Michelle O'Neill, the party's vice president, told RTÉ's Six One News that she wants to be "the First Minister for all the people" in Northern Ireland.
She added: "We have an Executive here that can put money in people's pockets, but that is being denied because the DUP are not accepting the democratic outcome of the election."
She accused the Democratic Unionist Party of being "in cahoots with the Tories in London" and "holding society here to ransom".
Ms O'Neill said she is "resolute" and "determined" that people in Northern Ireland will get the representation they voted for.
She will listen to the concerns of all parties, and there is "a landing zone that everybody can sign up to " but the DUP is refusing to cooperate.
Ms O'Neill said she has spoken to the Taoiseach, the Minister for Foreign Affairs Simon Coveney and British Prime Minister Boris Johnson this week.
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Earlier, it was reported that Mr Johnson will visit Northern Ireland on Monday amid a worsening political stand-off over post-Brexit trading rules.
"I've spoken with Boris Johnson himself. He will be here on Monday. I intend to put it to him directly that he needs to stop pandering to the DUP (Democratic Unionist Party)," Ms O'Neill told reporters.
It comes after the Stormont Assembly failed to elect a new speaker after the DUP said it would not support the process as part of its protest against the Northern Ireland Protocol.
The move will stop the devolved Assembly from being able to function.
UUP MLA Mike Nesbitt, one of the candidates for Speaker, was not elected in the cross-community vote.
His candidacy was backed by 51.9% of MLAs, but failed due to a lack of cross-community support.
SDLP MLA Patsy McGlone also failed in a bid to be Speaker, receiving 71.3% of the vote but also failing to receive sufficient cross-community support.
DUP leader Jeffrey Donaldson has said he is sending a "clear message" to the EU and the British government about resolving issues with the Northern Ireland Protocol.
His party said it is blocking the election of a new speaker at the Stormont Assembly, which means the devolved legislature will be unable to function.
The new 90 MLAs met for the first time in the Stormont chamber yesterday after last week's Northern Ireland Assembly election saw Sinn Féin emerge as the largest party for the first time.
The first order of business was for MLAs to sign the roll of membership, before the sitting was suspended for lunch.
The DUP had also said that it would not nominate for the position of deputy first minister, which prevents the forming of a new executive, as part of its protest against the protocol.
Unionists oppose the post-Brexit treaty because of the economic barriers it creates between Northern Ireland and Britain.
Sinn Féin's leader in Northern Ireland Michelle O'Neill described the DUP move as "disgraceful" and Alliance leader Naomi Long said it was "incredibly frustrating".
Speaking shortly before the plenary session began, Mr Donaldson said: "I believe that we need to send a very clear message to the European Union and to our government that we are serious about getting this protocol sorted out.
"Because of the harm it is doing, undermining political stability, damaging the agreements that have formed the basis of political progress made in Northern Ireland, to our economy, contributing to the cost-of-living crisis, this matter needs to be dealt with."
Ms O'Neill told MLAs the public is hoping that Northern Ireland's elected parties have "the maturity and courage" to take responsibility, adding that "there is absolutely no reason we should be in a rolling crisis, even for one second".
It is the job of politicians to "properly fund" the healthcare service and to agree a three-year budget and invest in the health service, Ms O'Neill said.
"This is our hour of decision, not tomorrow, and not for a moment longer can the DUP deny democracy, punish the public, boycott this Assembly and executive, and prevent us from putting money in people's pockets.
"Every one party in this chamber told the electorate that they would turn up on day one. Well, the DUP have failed on day one."
DUP MLA Paul Givan told the Stormont Assembly that his party would not be supporting the election of a speaker.
The Ulster Unionists nominated Mike Nesbitt and the SDLP nominated Patsy McGlone.
Mr Givan told MLAs: "The DUP received a mandate to remove the Irish Sea border and our mandate will be given respect. Our message is now clear, it is time for action, words will no longer suffice.
"It is because we want these institutions to endure that we are taking the action we are taking today.
"Northern Ireland works best when we work together. Those who now call for majority rule need to recommit themselves to the principles of the Good Friday Agreement.
"We will not be dictated to, we will be treated with respect and equality. Now is the time for action."
Alliance leader Naomi Long said her MLAs came to Stormont to elect a speaker.
"To turn up here, to sign in, to take salaries and to refuse to take seats is a slap in the face for every family that struggles to make ends meet, for every person who sits on a waiting list," she said.
"I would appeal to the DUP to think long and hard before they insult the electorate by doing so today." she added.
UUP leader Doug Beattie urged that an Assembly speaker be elected so that the public's concerns can be addressed.
After standing in silence before MLAs for several seconds, Mr Beattie said: "Silence. The same silence we were subjected to for three years when Sinn Féin walked out. The same silence we're now going to be subjected to if the DUP don't support a speaker."
SDLP MLA Matthew O'Toole accused the DUP of "demeaning democracy".
"In stifling the creation of an executive and the election of a speaker, the DUP has demeaned the entire democratic process. Shame on them," he said.
Traditional Unionist Voice leader Jim Allister said it was not appropriate to nominate a speaker to the Assembly while the Northern Ireland Protocol is in place.
Outgoing speaker Alex Maskey thanked his Assembly colleagues, as well as his family, in a speech to the Assembly.
He also told MLAs that politicians in Northern Ireland had come through political difficulties before.
Mr Maskey said: "I recognise that we are currently in a difficult political situation. Since 1998, we have all seen our fair share of those. Those of us who were here in 1998 and since then had big issues to deal with. However we did come through them.
"The last two years we were able to meet the challenges of getting the Assembly re-established and keeping the Assembly functioning to take important decisions during the pandemic."
Earlier, The Taoiseach said he is disappointed by the DUP's decision to block the election of a speaker.
Micheál Martin described the move by the DUP as "unsatisfactory".
"I think the people elected an Assembly and the Assembly should meet and then the Assembly should form an Executive," he said.
The British secretary of state for Northern Ireland said it is "disappointing" that a new speaker has not been nominated for the Assembly.
"Great to have MLAs back in Stormont today, but disappointing to see a Speaker has not yet been nominated," Brandon Lewis tweeted.
"The people of Northern Ireland voted and deserve a stable and accountable devolved government. I urge the parties to come together and form an Executive," he added.