Mansa SSP Mukhwinder Singh said police have arrested three accused Balbir Singh, Hardeep Singh, and Sadhu Singh from the district on a tip-off.
He said efforts are on to nab three other accused-- Amandeep Singh, Babrik Singh and Sita Singh.
A case of murder had been registered against the six, one of whom is a Dalit, in connection with the incident.
Police said the incident was a fallout of inter-gang rivalry and that the two groups had been involved in clashes in the past too.
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"Then they attacked Sukhchain and his friends with sharp-edged weapons on Monday night. Though Sukhchain's friends managed to flee, the other group brutally killed Sukhchain with sharp-edged weapon," the SSP said.
His body was recovered from the house of Balbir, one of the accused, police said.
There were injury marks on the body and leg was also found chopped off, police said, adding the missing limb has been found in the fields, nearly 400 meter from the crime scene.
"We shall now request the family of victim to cremate the body," the SSP said.
He said two persons of the rival group, who are not named in the FIR, have been rounded up for questioning.
The incident drew condemnation from the opposition Congress, which alleged the perpetrators had links to the ruling Akali Dal.
PCC chief Amarinder Singh, locked in a bitter war of words with the Akali leadership, cited media reports to claim that two of the accused had links with the ruling party. He said they were the nephews of Gharanghna sarpanch whose father was the driver of the Punjab Chief Minister.
"These developments can have serious consequences for the future of Punjab," he warned, adding the Badal government was "meticulously destroying" the secular character and peaceful environment of the state.