The first such graffiti appeared on the walls of historic Hariparbat Fort in the old city last week. "Welcome Taliban, Go India Go Back" were the words written across the wall of the Fort, which incidentally has a CRPF camp guarding it.
Flags of Pakistan and Lashkar-e-Taiba militant outfit were also hoisted on the wall, they added.
Police have registered a case in this regard and questioned several suspects but so far no arrest has been made in the case.
"This is an unnecessary nuisance spread by a few miscreants... They come in the dead of the night, paint a few walls and disappear," Bukhari said.
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He said police is, however, investigating the matter as these miscreants are vandalising public property and cultural heritage of Kashmir as in the case of the Hariparbat Fort.
Similar graffiti have appeared in other parts of the city with the latest one reported from old Barzulla, police sources said.
The sources said at many places, police has painted over the graffiti but new graffiti have been making an appearance every other day.
The police said graffiti had come up after several media reports suggested that Taliban might enter Kashmir after withdrawal of the US troops from Afghanistan next year.