"I want to tell my friends that the murder of Vipan Sharma which took place on October 30 on Amritsar-Batala road was committed by me... His killing should not be linked with any religion," said the post by Saraj Singh Mintoo.
Mintoo is wanted by the police in the murder of Vipan Sharma, a district chief of the group "Hindu Sangharsh Sena", who was shot dead at point blank range in full public view on the road between Amritsar and Batala, around 40 km away.
In his post, Mintoo accused Vipan Sharma of murdering a policeman who was his friend's father.
Mintoo has been charged in the murder along with two others, Shubham Singh and Dharminder Singh. All three are missing, the police say. A special investigation team led by Amritsar Deputy Commissioner of Police, Jagmohan Singh, is probing the murder case.
The police in Amritsar have asked their cyber-crime cell to verify the authenticity of the Facebook post.
"We have taken notice of the Facebook post," said senior police officer Charanjit Singh.
"We want to know whether the (Facebook) account actually belongs to the accused or somebody else is updating the posts," added Mr Singh, who is part of the special probe team.
The police have taken Sukhraj Kaur, Mintoo's mother, into custody for allegedly sheltering gangsters after the crime.