Sinn Féin President Gerry Adams says his party is not trying to undermine the Ceann Comhairle.
Opposition parties criticised Sean Barrett for cancelling a Dáil debate on a Commission of Inquiry into Garda malpractice.
The Ceann Comhairle said it may overlap with a High Court case being taken by Alan Shatter.
Fianna Fáil has called on Mr Barrett to withdraw claims that the Opposition is trying to undermine him.
Deputy Adams has said that responsibility for the cancellation of the debate lies with the Taoiseach.
"There's no plan by Sinn Féin to undermine the Ceann Comhairle," he said.
"There always has t be somebody who chairs the meetings and makes sure that everybody's within Standing Orders, and we may have concerns about how he did that, but the Taoiseach is the person who allowed the controversy to build, and refused to take a sensible approach."