The Society's executive committee, which met here, "expressed deep concern and anguish at the non-payment of advertisement bills of selected member publications for several years.
"This has caused severe financial distress to these newspapers as the media industry passes through a very difficult period," it said in a statement.
The Society urged Chief Minister Mamata Banerjee to clear the dues of its members without further delay.
It also expressed dismay at the reported stand of the government to not clear the dues of its predecessor Left Front government, saying this was a negation of constitutional principles.
The New Delhi-based INS, founded in 1939, plays a major role in protecting and promoting the freedom of the press in India.