Mary Lou McDonald and Sinn Fein TDs and officials are facing calls to stay away from the Dail for two weeks after they attended former IRA member Bobby Storey's funeral.
Ms McDonald, her predecessor Gerry Adams, deputy leader Michelle O'Neill and a number of Sinn Fein TDs and MLAs, including Pearse Doherty, attended the funeral of Mr Storey, a senior figure in the republican movement, in west Belfast which drew a reported crowd of around 1,800 people on Tuesday.
The large attendance came despite official guidance in Northern Ireland restricting the numbers who can attend funerals to 30 during the Covid-19 pandemic. The PSNI is reviewing footage of the funeral for any suspected breaches of regulations.
Sinn Fein mounted a robust defence of its actions yesterday amid mounting criticism.
First Minister, Arlene Foster, called on Deputy First Minister Ms O'Neill to apologise. However, Ms O'Neill told MLAs she stood by her actions.
Mr Doherty said he would not advise anyone attending the funeral to quarantine. "Neither would I encourage people who went to Tesco yesterday to quarantine either," he added.
However, Ceann Comhairle Seán Ó Fearghaíl has been asked to request that anyone who attended the funeral in west Belfast stays away from Leinster House for the next 14 days in line with public health advice.
Fine Gael senator Garret Ahearn has written to the Dail chairman saying such a request is "in the interest of everybody's health and safety". He wrote: "It would be extremely regrettable if a cluster of Covid-19 cases was created in Leinster House because some members travelled to Belfast."
Prior to the letter being sent, Mr Ó Fearghaíl told the Irish Independent: "It would be inappropriate for me to comment on something of this nature beyond saying I would expect all members of the Oireachtas to adhere in full to the Nphet guidelines."
Ms O'Neill told MLAs she stands by her actions and made it clear she would not be quitting over the controversy. She also declined to apologise to anyone who might have contracted Covid-19 as a result of being among the crowds.
She told members of Stormont's Executive Committee that the things the organisers could control - such as the size of the cortege and the numbers inside the church - were observed.
Ms O'Neill, who described much of the criticism aimed at her as "political point-scoring", said she would continue in her role as joint head of the devolved administration.
However, she said a selfie photograph that was taken of her and two other attendees at the funeral "should not have happened". She said it happened in the "blink of an eye" at the close of the commemoration at Milltown Cemetery.
Ms Foster, the DUP leader, said the executive's public health message had been damaged by what unfolded at the funeral.
A photo posted on Lucan Sinn Fein Facebook page of Michelle O’Neill posing for a selfie with two attendees at Bobby Storey’s funeral
A Sinn Fein spokesman said last night that Ms McDonald would not be commenting on the controversy.
Mr Doherty told RTE's 'SixOne News' there had been engagement with the PSNI and the church to comply with social-distancing guidelines, with numbers restricted inside the church and in the funeral cortege. "I believe the family and the local organisers did everything in their power to abide by the restrictions in place," he said.
Health Minister, Robin Swann, has said he believes Mr Storey's funeral breached Covid-19 restrictions around mass gatherings.