Speaking at Friday’s Assembly sitting – the first one since this year’s new cohort of MLAs were elected at the beginning of May – Ms O’Neill said: “Today I stand ready, we stand ready, to elect a speaker, form an Executive and take on the leadership of the Northern Ireland Executive, as a First Minister for all and a government that works for all of the people.”
Ms O’Neill and Sinn Fein politicians refer to Northern Ireland as ‘the north’ or ‘the north of Ireland’.
While different media commentators have been discussing the significance of Ms O’Neill’s comments, Mr Paisley told the BBC: "100 years to call Northern Ireland its proper name, my goodness, let me please lie down and recover from the shock of that.”
“I think it’s up to Sinn Fein to explain to people how they think using the proper and official term of the country which inside they live, and which gives them a salary, and which gives them the National Health Service, and which gives them the enjoyment of the liberties that they have - why it is such a big deal for them to use its proper name,” said the DUP MP for North Antrim.
“I don’t ask for any credit, or any pats on the back, or applause when I call the Republic of Ireland its proper name, but maybe that’s how trivial I should be, that now that I’ve used the proper terminology for my neighbouring state, that I should be awarded and applauded. I honestly think that’s quite juvenile by Sinn Fein.”
Mr Paisley further spoke to the BBC’s Stephen Nolan about his party’s calls for Boris Johnson and the UK government to scrap the NI Protocol, ahead of the UK Prime Minister’s visit to the region on Monday.
DUP leader Sir Jeffrey Donaldson earlier said: "I need action and that's how I will judge what the Prime Minister does, not necessarily what he says. I will judge what the Government does and I will look at the credibility of what that is and the impact it has in terms of removing that Irish Sea border.
"I haven't seen the Government's proposals so I'm not in a position to say I would do a or b, but you will note that in the past we have been reasonable, we have taken proportionate action, we have sought to give time for negotiations, to bring forward outcomes. That hasn't happened and I think the time has come now for action.
"If the Government takes decisive action then, of course, we will consider what steps we can take."
However, Ms O'Neill said parties do not need a "pep talk" from Mr Johnson, whom she claimed is "shoring up the DUP's bad behaviour".
She said: "The DUP are holding the rest of society to ransom because of their actions, because they delivered us the hardest possible Brexit, so I think Boris Johnson, perhaps, is speaking out of two sides of his mouth - on one hand he is saying he wants politics to work, he wants the Executive to be formed, at the same time he is feeding the instability and economic uncertainty with his threats to go around the protocol."