An image of the poster was circulated on WhatsApp and shared on social media with a caption claiming that a copy of it was spotted this morning at Jantar Mantar.
However, a police team searched the area and said no such poster was spotted.
The poster said "to shoot the traitors of JNU is a Rashtradharm (national duty). I shall shoot Umar Khalid, Anirban Bhattacharya and Kanhaiya."
The poster condemned Congress Vice President Rahul Gandhi and Delhi Chief Minister Arvind Kejriwal for their support to the JNU students.
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"I shall shoot all who celebrated the anniversary of Afzal Guru's hanging... The country faces more threat from traitors than terrorists... Such traitors should face life imprisonment," the poster read.
When asked, Deputy Commissioner of Police (New Delhi) Jatin Narwal said, "We have initiated an enquiry into the matter."
The person who picked up the call, claimed that he runs a shop at Yamuna Bazar area and that he had visited Jantar Mantar today.
However, he did not specifically respond to questions about whether he had pasted the poster. This man is likely to be questioned soon, the official added.
On March 7, Delhi Police arrested Adarsh Sharma, who claimed to be president of Purvanchal Sena which had announced through posters a reward of Rs 11 lakh for anyone who "shoots" JNU Students' Union president Kumar.