Speaking to reporters at Raj Bhavan, Dhankhar called upon those in position of power not to shirk responsibility as it is "no occasion to play politics".
"How can an elected head of a government use public money to give advertisement in national media that there will be no NRC, no CAB in state? This advertisement is unconstitutional," the governor said.
"As Constitutional head I had very gracefully invited her (CM) attention, I had urged her (to) withdraw it.
I am sure you all will agree that public money can't be used to lead an agitation against law of the land," he added.
Dhankhar, who described the law and order situation in the state as "unimaginable", said public property is being damaged in a wanton manner, ruthlessly and recklessly, and fear has been put in the minds of people belonging to a certain section of the society.
The governor has been at loggerheads with the Mamata Banerjee government over several issues.
Protests over the amended Citizenship Act continued to rock various parts of West Bengal for the third consecutive day while Internet services were suspended by the state government in six districts.