The Dáil has passed a Fianna Fáil motion calling for a change to the terms of reference of the scoping exercise into the death of Shane O'Farrell.
The family of the student from Co Monaghan, who was killed in a hit-and-run while cycling in 2011, have argued that the parameters of the inquiry are too narrow.
In February, Minister for Justice Charlie Flanagan appointed Judge Gerard Haughton to carry out a scoping exercise which would determine if a full inquiry was warranted.
In July, the minister rejected the terms proposed by the judge.
The purpose of the Fianna Fáil motion was to approve the original terms of reference.
Last year the Dáil voted in favour of setting up an inquiry into the death of Mr O'Farrell.
He was 23 when he was hit by driver Zigimantas Gridziuska, who had a string of convictions and was out on bail at the time of the incident.
The O'Farrell family said he should have been in prison at the time and blamed system and garda failings.
The motion, including a Sinn Féin amendment, was passed with the support of all opposition parties.
The Government voted against it.
Earlier this month the O'Farrell family accused the Department of Justice of delaying the setting up a public inquiry into his death.