The petition was set to be presented to the council last week, until a technicality was pointed out by Cr Glenys Dickson.
Cr Dickson moved that petition organiser Hayden McIntyre not be permitted to speak to it because Mr Parry’s appointment was an employment matter.
Mayor Ben Bell opened the floor for debate.
Cr Robert McKenzie questioned why the petition could not be spoken to.
Mr Bell agreed with him.
"While I may or may not agree with the petition, I still do feel like it should be the right of petitioners to speak ... but as I said before, there is a provision in the standing orders, as Cr Dickson rightfully pointed out," Mr Bell said.
Cr Neville Phillips moved that the mayor and councillors not receive the petition.
Cr Keith Hovell seconded the motion, saying it was "divisive and an unnecessary and unwelcome distraction".
Time taken because of petitions and emails had slowed him from undertaking important tasks in the community, he said.
The petition had gained 313 signatures, of which 18 were invalid as they were from addresses outside the Gore district.
It was put forward after the council offered Mr Parry the role while it looked for a new chief executive.
Mr Parry resigned in October after more than 20 years as chief executive.
But he was appointed as interim chief executive after the person designated to fill in as interim chief executive moved to another job.
Mr McIntyre said he was still gathering his thoughts after not being allowed to speak.
"There wasn’t a lot we could do, really," Mr McIntyre said.