She made the comment at her party's ard fheis (annual conference) in Dublin.

Sinn Féin became the biggest party at Stormont after an election in May, meaning Ms O'Neill is entitled to be first minister.

But the DUP's refusal to join an executive prevented her from doing so.

The DUP has said it will not return to devolved government until its complaints about the post-Brexit trading arrangement known as the Northern Ireland Protocol are addressed.

During her speech at the ard fheis, Ms O'Neill said the DUP was using its protest about the protocol as "cover".

"It is wrong that progress on the issues affecting the daily lives of people are being put on hold because one party refuses to accept the democratic outcome of last May's Assembly election," she said.

"At any time this would be unacceptable but in the middle of a cost-of-living crisis it is utterly disgraceful.

"As you all know the DUP are using the Brexit Protocol as cover not to enter power-sharing.

"The real reason is because as an Irish nationalist I will be at the helm as first minister and everybody knows it."

The DUP leader Sir Jeffrey Donaldson has previously said he accepts the outcome of the May election but will not change his stance on power-sharing until his issues with the protocol have been resolved.

Sinn Féin is the largest party in opposition in the Republic of Ireland

Sinn Féin leader Mary Lou McDonald gave the closing address at the conference.

She used her speech to criticise the Irish government parties but also hit at out at London.

"The British government dithering must end. They must immediately bring clarity, a timetable for concluding negotiations with the European Union and the restoration of the executive."

She said that the Stormont stalemate cannot continue and accused the DUP of refusing "to accept the result of an election and prevent the formation of an executive".

Speaking of the Northern Ireland Assembly election, she told the conference that "for the first time, a republican, a nationalist, a woman from Tyrone, was elected as first minister in a state designed to ensure that this could never happen".

Sinn Féin is the largest in opposition in the Republic of Ireland, where recent polls have pointed to rising support.

During her address, Ms McDonald referred to the governing parties in the Republic, Fianna Fáil and Fine Gael, as playing "political hokey-pokey".

"Change can't be stopped by Fianna Fáil and Fine Gael, now so joined at the hip that it doesn't matter to them which leader is taoiseach (Irish prime minister), so long as it's one of them," she said.

"Leo leaves, Micheál goes in. Micheál leaves next month, Leo goes back in.

"In, out. In, out."

Direct rule 'not an option'

Ms McDonald attacked the "chaotic" Conservative government.

"They can't run their own country without bringing it to the brink of financial ruin. They certainly have no right to tell the people of Ireland how to run ours.

"The Tories should leave governing of this island to the people who live here, and we'll shape a better future together.

"They must immediately bring clarity, a timetable for concluding negotiations with the European Union and the restoration of the executive.

"But whatever happens, be clear that a return to direct rule from London is not an option. Working together is the only way forward."

Until February Ms O'Neill had been Stormont's deputy first minister.

But when the DUP removed Paul Givan as first minister from the executive in protest over the protocol that meant Ms O'Neill could not remain in office either.

Her party won 27 seats in May's assembly election, with the DUP securing 25.

Sinn Féin has repeatedly called for an executive to be restored, saying the onus was on the DUP to "end its boycott".

During her speech in Dublin, Ms O'Neill accused the DUP and the Conservative Party of creating chaos and dysfunction at Stormont and Westminster.

She also criticised Northern Ireland Secretary Chris Heaton-Harris over his indecision about calling another Stormont election.

She called for his statement to the House of Commons next week to be definitive as "drip feeding is fuelling instability and uncertainty".

Ms O'Neill also called on the UK and the EU to "propel the protocol talks" and demonstrate will to find a solution.