The vice-president of Sinn Féin, Michelle O’Neill, has said that efforts to resurrect Northern Ireland’s assembly at Stormont will continue, after the Democratic Unionist party (DUP) blocked a second attempt to elect a new speaker.

The DUP is maintaining its position that it wants to see action from the UK government over the Northern Ireland protocol before backing a new speaker, which would enable the assembly to start fully functioning again. It described the recall of the assembly on Monday as a “stunt”.

The two nominees for the role – the Ulster Unionist party’s Mike Nesbitt, and Patsy McGlone, from the Social Democratic and Labour party (SDLP) – failed to secure the necessary cross-community support from members of the legislative assembly (MLAs).

The plenary session of the assembly was then suspended as business cannot be carried out without a speaker. MLAs were in the chamber on Monday after Sinn Féin’s recall petition to elect a speaker and deputy speakers, and to appoint a first minister and deputy first minister.

After the session, O’Neill told media in the Great Hall: “We had our second attempt today to try and get things up and running but unfortunately the DUP standoff continues.

“We will come back again. We will do this again, because I’m not giving up. I believe in making this institution work.

“The DUP are punishing the public. It is the public who are missing out. It is the public who are being held to ransom because of their actions.

Sinn Féin proposed a recall last week, supported by the Alliance party and the SDLP, but a new speaker and the first and deputy first ministers cannot be installed without the DUP’s support.

Under assembly rules, no business can take place after an election until a new speaker is elected. An attempt to do so on 13 May failed because it requires cross-community support from a majority of unionist and nationalist MLAs.

Earlier on Monday, O’Neill told the chamber: “The people have spoken and they want action, not protest. They want the parties and every single MLA elected to this democratic institution to get their sleeves rolled up and to get down to business.”

She added: “The DUP’s standoff is with the public and not with the European Union. As I stand here today I am ready to work with others.”

The DUP’s Paul Givan told the MLAs: “The public will see the hypocrisy for what it is from Sinn Féin.

“This isn’t a serious attempt to restore the principles of power-sharing and these institutions. It is a stunt.”

The Alliance party MLA Nuala McAllister said a restored assembly at Stormont could begin to tackle the cost of living crisis, adding: “Those of us who want to get on with the job are more than desperate to do so.”

Unionist politicians have protested against the protocol, a part of the UK-EU Brexit deal that keeps Northern Ireland aligned with the EU’s single market for goods.

This was designed to ensure free trade could continue across the Irish land border after Brexit but it has resulted in additional checks being placed on some goods moving between Great Britain and Northern Ireland.

The SDLP MLA Matthew O’Toole said the number of MLAs who supported the Northern Ireland protocol had increased in the recent assembly election.

“Why is the DUP holding the people of Northern Ireland hostage? They say it is all about the protocol,” he said. “The protocol is an international treaty signed between the UK and the European Union.”

The Ulster Unionist MLA Robbie Butler said his party wanted all-party talks to begin on a programme for government.