Both leaders held separate meetings with the public at the party office here while hearing their grievances.
Akali councillors approached Parkash Singh Badal, the ex-chief minister, in the morning and told him how Congress leaders were "threatening and attacking" them, a release from SAD said.
Kharar leader Ranjit Singh Gill claimed a Congressman Jeeti Padiala allegedly entered the residence of Kurali committee president Krishna Devi and took away councillor Ramakant at gun point.
Badal talked to DGP Suresh Arora over the issue and told him that it was unfortunate that such violence was being perpetrated against an elected official, the release said.
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It added that a family approached SAD president Sukhbir Badal and claimed that they were not able to get justice in a murder case.
Meanwhile, the former chief minister said the Centre's reported decision to extend concessions to Punjab's neighbouringhill states will hit the state and its economy.