There was also support from politicians while police in various cities said they had stepped up security around the homes of players.
A day after an effigy of Ganguly was burnt on the streets of Calcutta, cricket fans in his home city released pigeons in a symbolic gesture of support for the Indian captain.
India, one of the pre-tournament favourites, scored just 204 runs in their opening victory over minor nation the Netherlands before losing by nine wickets to Australia on Saturday in South Africa.
"Pride of India, Pride of Bengal, we are with you Sourav," demonstrators chanted in Calcutta, holding up placards saying: "Tiger of Bengal, cheer up".
Pradip Prasad, the leader of the Tuesday's demonstration, said: "Stop it. That is our message to those who are burning the effigies of Ganguly, attacking Kaif's home and set fire to posters of other players."
The house of middle-order batsman Mohammad Kaif in Allahabad had been smeared with black paint and oil on Sunday by fans angry at his poor form.
In
"At the moment we have increased patrolling in the area where Sachin lives," said joint commissioner of police Javed Ahmed. "We are taking every precaution."
In Bangalore, security has been stepped up at the houses of vice-captain Rahul Dravid, paceman Javagal Srinath and leg-spinner Anil Kumble as "precautionary measure", police said.
PARLIAMENTARY SUPPORT
The team also found support in the country's Parliament.
"This team belongs to India. It is very unfortunate that Kaif's house was attacked," opposition lawmaker Priya Ranjan Dasmunshi said.
Speaker of the house, Manohar Joshi, a former cricket administrator who travelled to Centurion to watch the India-Australia clash last week, said the country needed to be proud of its team.
"The government should ensure that they (players' homes) are given full protection," Joshi said. "The entire house sends its good wishes and this message will be conveyed to the team."