Ms McDonald has effectively assumed the role of acting leader of the party given the strong likelihood of an election before Christmas, without a vote being cast.
Speaking to the media at Leinster House, Mr Doherty said Tánaiste Frances Fitzgerald’s position was now untenable and she “needs to go” if the election is to be avoided.
“It is very clear that the position of the Tánaiste and former minister for justice is untenable.
“She continued to express confidence in the Garda commissioner Nóirín O’Sullivan despite her knowledge of a smear campaign against Maurice McCabe,” he said.
“A smear campaign of the most unimaginable kind and information that did not stack up.
“That is why her position is not tenable and she has to go. She has serious questions to answer, she failed to answer those questions and we need to hold this Government to account.
“Let’s be clear here, if this government wants to avoid an election, then the Tánaiste needs to go,” said Mr Doherty.
“What we have here is a dysfunctional government presiding over a crisis in housing, in childcare and in policing. In all of this there has been no accountability. From day one, our job as an opposition party has been to hold the Government to account and that is exactly what we have done and we make no apology for that,” Mr Doherty said.
In relation to the party’s leadership, he confirmed that Ms McDonald will lead the party into the election, making it all but certain that she will succeed Gerry Adams as president when he formally steps down next year.
“Mary Lou McDonald will lead our campaign into the election, if there is to be an election,” he said.
“That is a decision for Leo Varadkar as to when it happens,” he said.
“She is the deputy leader of the party, she was just re-elected. Gerry Adams is not contesting the next election so therefore it is automatic that Mary Lou would lead our campaign.
“It is not our intention to cause an election on foot of our motion of no confidence but if Leo made it about an election, then we in Sinn Féin are ready for that election and will fight it on the issues,” said Mr Doherty.
“We are very relaxed about the transition and electing a new party president and that is something our ard comhairle will deal with in due course. We are very satisfied we are in a strong position to fight this election,” he said.
Mr Doherty said the party is not considering putting down a motion of no confidence in current Justice Minister Charlie Flanagan, who himself is in the firing line over his role in the McCabe email saga.
“We have no intentions of putting down a motion of no confidence in Charlie Flanagan at this stage. That is not to say if information came into the public domain that brought Charlie Flanagan centre stage that that would not happen. We would reassess the matter at that time,” he said.
Mr Doherty has long been seen as a leadership candidate himself but he ruled himself out last week of contention saying he has a young family and the time is not right for him.
Meanwhile, the Independent Alliance has told Leo Varadkar and Micheál Martin to “swallow some pride” and not bring the Government down by causing “a completely needless election” over “a spat about an email”.
Transport Minister Shane Ross said a solution must be found “as a matter of urgency” as he said the Alliance backs Frances Fitzgerald “100%” but denied he is in effect telling Fianna Fáil to back down.
“No, I’m not saying that. I’m saying they should come to a decision. This isn’t about backing down. If it means someone will have to swallow some pride, well then that’s what they have to do,” he said.
The view was shared by the four other Alliance TDs.
Minister of state for disabilities Finian McGrath — who introduced himself as “the Independent TD for Dublin Bay North” in a nod to the possibility of an election — said that “we want to get on with our job” while Mr Ross denied the Alliance wants to avoid an election due to fears they would be wiped out.