Addressing a press meet here on Saturday, Dasmunshi said that freedom of speech and expression was guaranteed by the Constitution and it would be an injustice to art and they should let the people decide on the film.
The minister also asked Gujarat Chief Minister Narendra Modi to consider his appeal "sportingly" and said that the state government should respect the creative contribution of directors and actors.
Speaking further Dasmunshi affirmed that Aamir had not stated anything which could be assumed as against of the people of Gujarat or the Sardar Sarovar dam project.
However, he said that following the orders of the Supreme Court on the rehabilitation process there was no change in the Centre's policy on the Sardar Sarovar dam.
Aamir's latest movie has been reportedly facing ire of Bharatiya Janata Party (BJP) following his remarks on Narmada Dam project.
Aamir was criticised by both BJP and Congress as he supported the Narmada Bachao Andolan, which was spearheading a movement in the Narmada Valley for proper rehabilitaiton.
Fearing attacks on theatres in the state, the Multiplex Association of Gujarat on Tuesday decided not to screen the film multiplexes across Gujarat.
On May 25, senior BJP leader Vijay Kumar Malhotra had said that BJP was willing to put an end to the row over Fanaa if Aamir Khan apologised for his comments on the Narmada Dam project and the recent Vadodara demolition.
However, Aamir Khan had already refused to apologize on Friday and said "I haven't done anything wrong, so why should I apologize?"
"The point is that people affected by the dam need homes and a livelihood." he added.
In April, Aamir had supported the demand of Narmada Bacaho Andolan and other anti-dam activists and urged the centre government to stop work on the project until villagers and farmers are adequately compensated.
The Kunal Kohli-directed movie, made under the Yash Raj banner, is packed with stars like Aamir Khan and Kajol, and was already making waves before its release.
Fanaa which was released on Friday is also the comeback film of actress Kajol.