Sinn Féin's Louise O’Reilly has called on the Taoiseach to remove the Minister for Justice, Helen McEntee from office.
If that does not happen Sinn Féin will look at all options including a no-confidence motion, she said.
The party cannot table a motion next week but it could do so the following week.
Social Democrats Dublin Central TD Gary Gannon said he did not have confidence in either the Justice Minister or the Garda Commissioner.
He called on Minister McEntee to come before the Dáil next week and to answer questions about the events in Dublin city on Thursday.
He said the policy of "appeasement" towards far-right protesters had to end because they believe they can act with impunity.
Labour Leader Ivana Bacik said there has to be more gardaí deployed on the streets and there are major problems around garda recruitment.
She said Labour has not had confidence in the Government's handling of policing for some time.
The Justice Minister is likely to face questions about the recent street violence in Dublin when she takes the place of the Taoiseach on Wednesday during Leaders' Questions in the Dáil.
Earlier, the Tánaiste and Minister for Foreign Affairs Micheál Martin has said he does have confidence in the Minister for Justice Helen McEntee and Garda Commissioner Drew Harris.
Speaking in Cork city this morning, he said the Government's priority now was protecting citizens first and foremost, and supporting An Garda Síochána.
In the wake of the riots in Dublin city centre on Thursday night, Sinn Féin leader Mary Lou McDonald had said she did not have confidence in either the Minister or the Garda Commissioner.
Ms McDonald said that the Government and Garda Commissioner had been warned repeatedly for "a very long time" that there was a problem in terms of safety in Dublin city centre.
This morning the Tánaiste said this was not a time to be undermining gardaí or its leadership because the State essentially came under attack last Thursday evening, in the context of public transport being attacked, buses being burned, drivers and gardaí being attacked, and shops being looted.
"All of this is essentially an attack on the state and an attack on families, on workers and on our communities and society and we cannot tolerate that," he said.
The Government’s focus now, he said, is on dealing with threats to public order because it has an obligation to protect citizens across the country,
"We also have to deal with the rapid mobilisation of people across social media platforms and the organisation of such rioting and such unacceptable behaviour," he said.
Mr Martin also said there is no need to recall the Dáil on Monday. "Essentially we as citizens need to reclaim our streets—as we head into the busy Christmas period which is so important for businesses and workers, we are not going to cow down to those who want to undermine the State," he said.
Concerns over social media abuse towards immigrants
The Tánaiste said he was very concerned about the level of abuse and hatred that is being directed towards immigrants on social media, adding that the level of hatred and bile on some social media platforms from some minority groups is "absolutely unacceptable".
Hate legislation is being brought in in relation to this, he said, adding that robust engagement was needed with some social media platforms in terms of their facilitation of such online abuse.
"Thankfully in Ireland we are a multi-cultural society where our population and economy has grown and are a modern progressive and inclusive society which is worth fighting for and protecting and worth recommitting ourselves to," he said.
"We have people from all nationalities working in our hospitals, and children of all nationalities in our schools, and likewise we have Irish people working all over the world," he added.
He said people must not be intimidated by the kind of narrative that is witnessed online "which the vast majority of Irish people have no time for who believe in freedom of speech of opinion, of mobility and inclusivity."
Additional reporting by Cathy Halloran
