The appeal comes amid demands from tobacco companies for reconsideration of the government order to have pictorial warnings on both sides and covering 85 per cent of the pack.
Representatives of women groups, youth associations, hospitals, self-help groups and voluntary organisations were among those who sent 4000 signed letters to the PM.
Various eminent international public health organisations working on tobacco control and cancer issues had earlier written to Modi and Health Minister J P Nadda on the issue.
The move had made India a top ranker in terms of display of caution on packages.
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"India has become a trend-setter for neighbouring and many other countries on pack warnings with this announcement," said Bhavna B Mukhopadhyay, Executive Director of Voluntary Health Association of India.
Pakistan's Health Ministry on February 11 had announced new pictorial warnings covering 85 percent of the cigarette pack on both sides from the current 40 percent.
"Former Maharashtra Home Minister R R Patil's who passed away Feb 16 undergoing treatment for an advanced form of oral cancer raises concerns about gutka and cigarette use," said Mukhopadhyay.