Chairperson of the committee Francois Beukman said on Saturday they did not want to continue to see instability in the top leadership of the SAPS.
Beukman said the committee would discuss the matter during the police budget vote this month. He said this was the position they had been pushing for some time, and were insisting on the appointment of the new commissioner soon.
“In the past we have emphasised this. It's critical in terms of the stability of the police that the position of the national commissioner is filled,” he said.
Beukman said they understood that new Police Minister Fikile Mbalula wanted to prioritise the matter, and would support him in that.
He said if no appointment was made by October this year it would be two years that the SAPS had been without a permanent head.
Mbalula’s spokesperson, Vuyo Mhaga, declined to comment on the matter.
He said the ministry did not want to comment on it at this stage.
Phiyega was suspended in October 2015 after the Marikana inquiry asked that she be investigated for fitness to hold office.
Since then a board of inquiry into her found that she was not fit to hold office, and recommended she be fired over the Marikana tragedy.
However, Phiyega has challenged the findings of the inquiry in court.
She has maintained her innocence and said she was on the job for only two months when the Marikana events unfolded.
The fresh calls for the appointments of the new head of the police came as the Independent Police Investigative Directorate (Ipid) appealed for more funds from the committee to investigate police officers implicated in the Marikana massacre.
The report into the Marikana tragedy fingered some of the officers who were present at the scene and recommended they be probed for their conduct.
Ipid said it wanted R5-million to investigate the officers. However, the unit have hit a brick wall with the National Treasury to get the funds.
Beukman said Marikana was a non-negotiable and its recommendations must be fully implemented.
He said they would seek a meeting with the National Treasury to resolve the problem so Ipid would be able to conduct its business.
He said it was unfair that the police watchdog was being deprived of the resources it required to conduct an investigation into the Marikana officers.