Pargat was among the seven MLAs who were to be inducted as CPS in the 117-member state Assembly. Polls are due in Punjab early next year.
While the remaining six that includes four Akali MLAs and two from ally BJP were administered oath by Chief Minister Parkash Singh Badal at a function here, Pargat stayed away from the event.
Pargat has reportedly written to Badal and declined to take oath as CPS, while maintaining that he wanted to continue and concentrate as MLA only.
The Akali MLA had earlier protested against some issues pertaining to his Assembly constituency, including setting up of a waste treatment plant.
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Pargat, who was not available for his comments, has been opposing establishment of solid waste management plant in Jamsher village in his constituency in Jalandhar.
Two days back on the recommendations of the Chief Minister, Punjab Governor Kaptan Singh Solanki had given his approval for the induction of seven new CPSs.
Two BJP MLAs who were administered oath as CPSs are Sukhjeet Kaur Sahi (Dasuya constituency) and Seema Kumari (Bhoa constituency).
The Governor had earlier also accorded approval to drop Akali MLA Inderbir Singh Bolaria (Amritsar South constituency) from the post of CPS after he raised a banner of revolt opposing the state government's proposal to set up a waste plant in his constituency.
Before the new appointments, Punjab had 19 CPSs including Inderbir Singh Bolaria.
Meanwhile, reacting on Pargat Singh's refusal to be inducted as CPS, Chief Minister Parkash Singh Badal said any political party is like a family and MLA its member.
Badal said that Singh had some issue pertaining to his constituency but there is no question of any disquiet or unhappiness within the party.
"If he still nurtures some grudge in his mind, that too will be resolved amicably at the party level," Badal said On the sidelines of the function.
Justifying the need to induct six new MLAs as CPS, the CM said it was an exercise to enable them have a far better understanding of the democratic functioning of the government.