Pardhan's son Preetinder Singh told PTI that his father had late last night sent the resignation letter to party secretary and spokesman Daljit Singh Cheema after the ruling SAD asked him to resign on moral grounds.
Earlier, Cheema had said that party president Sukhbir Singh Badal has asked Pardhan to resign on moral grounds.
As the party high command could not contact him as his phone was switched off, the decision had been conveyed to the family of Pardhan, he said.
"He has faxed the resignation to party high command," Preeetinder said.
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Pardhan is a co-accused along with his accomplice Paramjeet Kaur and her son Harpreet Singh for allegedly killed Harpreet's wife Parampreet Kaur.
The Punjab government has formed a special investigation team (SIT) to probe the murder of Parmpreet.
"Patiala Police has arrested two accused, including the deceased's husband Harpreet Singh and her mother-in-law Parmjeet Kaur. We have secured their police remand for one day and would produce them in court today. The SIT has started its investigations," IG (Patiala zone) Parmjit Singh Gill had said.
Rural Development and Panchayats Minister Surjit Singh Rakhra had played a key role in helping Pardhan secure the top post after the Patiala Municipal Corporation elections last year.
Pardhan was appointed Mayor on September 17 but within a couple of months, his relations with Rakhra got strained.