The council president Sadhan Das said, "For the moment we are deferring the strike. We have been told the government will shortly take a decision on fare hike."
He said 30 per cent of the private buses were off the roads as the owners were unable to bear the losses due to non- revision of fares.
However, CITU, which also called a transport strike on the same day, maintained that will go on the strike.
A CITU leader said they were sticking to the strike call protesting the rise in diesel and petrol prices.
The INTUC, meanwhile, said it is not supporting the CITU strike.
Chief minister Mamata Banerjee has threatened to take stern action against bus owners participating in the strike saying that their licenses would be cancelled.
State transport minister Madan Mitra said the government would make all attempts to foil the strike called by CITU.