Members of the Dáil (lower house of the Irish parliament) are voting on a motion of confidence in the Ceann Comhairle (speaker).
Verona Murphy, previously a member of the regional independent group who now support the government, was elected as the first female Ceann Comhairle in December.
Sinn Féin leader Mary Lou McDonald said Murphy “lacked impartiality” and that her position was “untenable”.
In a statement, Murphy said she “categorically rejects these totally unfounded allegations” and “fully intends to continue” in her position.
Other opposition parties, including Labour and the Social Democrats, are also expected to vote no confidence in the Ceann Comhairle.
However, with the support of the government, which has a majority in the Dáil, Murphy is expected to survive the vote.
Murphy’s tenure as Ceann Comhairle has been dominated by a row over speaking rights in the chamber of the Dáil.
Four members of a government-supporting regional independent bloc have demanded that they be allocated time to question the government.
The government drew up plans to facilitate the four TDs (members of parliament), whose colleagues are part of the coalition.
Opposition parties have accused Murphy of not properly applying the rules of the Dáil in the lead-up to a vote on that proposal.
The Dáil has had to be suspended several times in recent months with the outbreak of rowdy scenes and TDs trying to shout Murphy down.
Murphy has described the behaviour of TDs as “an absolute disgrace”, accusing them of “making a holy show of yourselves”.
Taoiseach (Irish prime minister) Micheál Martin accused Sinn Féin of making “false claims” and said the party was trying to “undermine this institution”.
“Sinn Féin will not run this House,” Martin added.
It will be the first time that a Ceann Comhairle has faced such a vote in the history of the Dáil.