Ravinder Gosain, 60, was returning home after attending a morning drill at RSS shakha when he was attacked, they said.
Gosain died on the spot while the attackers fled, the officials said.
A three member special investigation team led by Deputy Commissioner of Police Gagan Ajit Singh has been formed to crack the case. The other members of the team are Sandeep Garg and Rajvir Singh, both additional DCPs, Ludhiana Police Commissioner R N Dhoke said.
Yash Giri, city secretary of the RSS condemned the incident and said it was "definitely a target killing".
"The victim was in Sangh uniform and about to enter his house when the killers targeted him," he said.
Police said they were examining CCTV footage from the cameras installed in the locality to get a clue about the culprits. Two suspects, with their faces covered, on a bike could be seen in the CCTV footage, they said.
"We are working on various theories. Police teams have been dispatched to various places in search of the killers," Dhoke said.
Investigations were underway, he said adding that it would be premature to term the incident as "terrorist crime".
The issue of the RSS activist's killing was raised by Home Minister Rajnath Singh, who was in Punjab, with Chief Minister Amarinder Singh.
"Union Home Minister Rajnath Singh has taken up the matter of the brutal killing of RSS leader Ravinder Gosain with Punjab Chief Minister Capt Amarinder Singh," former Punjab BJP chief Kamal Sharma said in a release.
Rajnath Singh told the Punjab chief minister to get the matter thoroughly investigated in a speedy manner, Sharmasaid.
Significantly, last year, another senior RSS leader Jagdish Gagneja died after he was shot by bike-borne assailants in Jalandhar.
The incident also comes at a time when the BJP has been protesting against the killing of RSS and its own workers in Kerala.
Opposition parties, the BJP and the SAD, strongly condemned Gosain's killing.
Punjab BJP chief and Union minister Vijay Sampla alleged that the killing proved that the law and order situation had deteriorated in Punjab.
"His murder is reminiscent of the black days of terrorism," said Sampla while demanding security for RSS and BJP leaders.
I have taken up this issue with Punjab Governor V P Singh Badnore who told me that a report on this matter has been sought from the home secretary, said Sampla.
"It is an unfortunate incident and we strongly condemn it. It is an attempt to disturb the communal harmony in Punjab," SAD spokesperson, Daljit Singh Cheema, said.
The state government should take this incident seriously and those responsible for this heinous crime should be put behind bars, demanded Cheema, a former minister.
Photograph: ANI
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