Tánaiste Leo Varadkar has criticised Sinn Féin leader in the North Michelle O’Neill for travelling from Belfast to Dublin for the vote on the Taoiseach last weekend.
Mr Varadkar said he did not want to comment directly on the controversy surrounding the funeral of Republican Bobby Storey.
However, the Tánaiste said politicians should “lead by example” and adhere to the rules and regulations they expect the public follow.
“I do think there was a huge contrast in what we saw last Saturday, where the Taoiseach Micheál Martin became Taoiseach and his family could not travel from cork to be with him,” he said.
“In contrast, Michelle O’Neill turned up for the photo-op. It does show a different attitude to public health. Sinn Féin are different to other parties but not in a good way,” he said.
The PSNI are currently investigating whether any rules were broken by those involved in Mr Storey’s funeral.
Meanwhile, the DUP has also called for Ms O'Neill to stand down as Stormont deputy first minister while the police investigate alleged social distancing breaches at Mr Storey's funeral.
DUP MP Jeffrey Donaldson claimed that Sinn Féin has "failed to read the public mood on this."
"I think now is the time to step up and demonstrate respect and integrity," he told the BBC.
"The law on these matters is clear and what happened at that funeral has sent out a very, very bad message to people in Northern Ireland.
"In light of the failure of Sinn Féin yesterday to grasp the opportunity to apologise, it is our view that the deputy first minister must now step back from her role while these matters are investigated by the PSNI.
"We will be asking the standards authorities in the Assembly to examine whether those MLAs who attended the funeral broke the code of conduct for MLAs, and we will also be asking the PSNI to specifically investigate any potential regulatory breaches by executive ministers including the deputy first minister.
"Given the seriousness of this situation, given the need to rebuild public confidence, given the need to have clarity in the Executive message on Covid-19 and the risk to the public, then yes that's what we believe should now happen."
A Sinn Féin spokesperson said: "Michelle O'Neill will not be stepping aside as deputy First Minister under any circumstances.
"The funeral of Bobby Storey was organised in accordance with his grieving family's wishes.
"The organisers did everything they could to ensure regulations were met and if it was not for the plan that organisers put in place with the PSNI to limit numbers then there would have been even bigger numbers in attendance."
Separately, Mr Varadkar defended his decision to overlook some of his key allies when allocating ministries of State.
He his authority has “absolutely not” being damaged by appointing TDs above people who were central to his leadership campaign.
“In terms of the appointments that I made as leader of Fine Gael, we had to go from something like 28 ministers, a very unusual situation, down to what would be more normal in a coalition something like 14,” he said.
“I picked the best people for the job, obviously you have to take into account issues like geography and gender and so on but the overriding consideration was the best people for the job,” he added.
The Taoiseach said former Housing Minister Eoghan Murphy asked not to appointed as a minister.
“I had a few drinks with Eoghan last night. We're still very good friends and he's full of ideas and thoughts for the future,” he added.
Mr Varadkar said he and former Education Minister Joe McHugh are “good friends” who “go a long way back”.
He said Mr McHugh wanted a European Affairs role but this was not possible as the position was allocated to Fianna Fáil.
Instead, the Donegal TD will be appointed chair of the Oireachtas Committee on European Affairs.
Mr Varadkar said Wexford senator Michael D’Arcy would have been a minister but “unfortunately he didn't hold a seat”.
When it comes to the deaths of those associated with Sinn Fein and the IRA, I don't adhere to the convention that one should postpone speaking ill of them.
The PSNI is reviewing video footage of the funeral of senior republican Bobby Storey - which was attended by prominent figures in Sinn Féin - for any suspected breaches of social distancing rules.