The "stink of cronyism" surrounded the Fine Gael Seanad byelection controversy, Sinn Féin deputy leader Mary Lou McDonald told the Dáil.

"When the Government took office in 2011, it promised a departure from the stroke politics and cronyism which had permeated past Fianna Fáil administrations," she said. "At the time, An Taoiseach went so far as to describe the election of this Government as a democratic revolution."

Nevertheless, Ms McDonald said, Mr Kenny had clearly bought into the politics of the past with his nomination of John McNulty to the board of the Irish Museum of Modern Art in order to facilitate him as a Fine Gael candidate in the upcoming Seanad byelection.

Ms McDonald, who was speaking before Mr McNulty's resignation from the board, challenged Tánaiste Joan Burton to say if she supported Mr Kenny in his actions and if her Labour colleagues would vote for Mr McNulty in the Seanad byelection.

Ms Burton said the practice had been that if a vacancy arose in the Seanad from one of the Government parties, that party would nominate someone to fill it. "Deputy McDonald would be familiar with the parallel practice for city and county councils, as well as the European Parliament," Ms Burton said. "When people from the deputy's party have stood down and a vacancy arose, the party would have nominated people to fill it."

The Tánaiste said they were talking about a standard practice relating to the filling of casual vacancies in city councils and the European parliament. Fianna Fáil and Independents had followed the same practice, she said. “The nomination is a matter for the Fine Gael party, its leader and its members,’’ Ms Burton added. “It is not a matter for the Labour Party, but rather it is for Fine Gael.’’

Ceann Comhairle Seán Barrett intervened to say there was a long-standing practice that Seanad business ought not to be discussed in the Dáil. He had allowed latitude because it was Opposition leaders’ questions.

Ms McDonald said she had raised something entirely different with Ms Burton. “I asked the Tánaiste if she approves of and supports the actions of An Taoiseach in using an appointment to a State board to create qualifications for his candidate for an election,” she said. She said the Tánaiste had described a process of co-option, which was not the case in a Seanad byelection. “That is an election.”

Mr Barrett said asking people for whom they were going to vote was not acceptable. "The deputy should resume her seat," he added, "she is over time."

Ms McDonald said the Ceann Comhairle was deliberately preventing her from asking the questions she wished to put. “I am applying the rules of the House, in case the deputy does not understand them,” she added.

Ms Burton said Ms McDonald was not addressing her party’s ardcomhairle, “where she might choose to tell people how to vote or else”.

She said the Sinn Féin deputy leader was speaking in the Dáil and that she had no right to direct people of any party or none as to how they were to cast their secret ballot. “It is quite impertinent of her to suggest how members of the Dáil or the Seanad should vote.”

When the Tánaiste said Ms McDonald had also raised questions about the museum board appointment, Mr Barrett said she was over her allocated time for a reply and should resume her seat. Ms Burton sat down.