Two farmers have been arrested in connection with the deaths, even as forest officials said that two heads of cattle belonging to farmers in the area had been killed by tigers last month.
The discovery of three carcasses - of a female and two cubs "in various stages of decomposition" - came days following the finding of a dead four-year-old adult male on Sunday near Golvali village in North Goa's Sattari sub district located in the lower reaches of the Western Ghats.
"In all, we have discovered four carcasses. Two arrests have been made. Both the arrested persons are farmers," a senior Forest Department official said.
According to Goa's Chief Wildlife Warden Santosh Kumar, a few weeks back, a motion sensor camera installed by Forest Department officials had snapped a tigress with three large cubs in the vicinity where the carcasses were found.
"Around two to three weeks back, our camera trap had captured a tigress with three cubs. It is believed that this family may have consumed some poisoned meat. We have intensified operations to check if the others are fine," Kumar added.
The post-mortem on the tiger found dead on Sunday had indicated that it was poisoned to death. Chief Minister Pramod Sawant had expressed shock at the tiger's death.
State Health Minister and local MLA Vishwajit Rane on Wednesday requested Union Environment and Forests Minister Prakash Javadekar to send a central team to conduct a detailed investigation into the matter, even as the Opposition has lashed out at the BJP-led coalition government for paying lip-service to protection of fauna and environment.
"With reference to the two cubs that have been found dead at Mhadei Wildlife Sanctuary, Sattari, I would request Union Minister for Forest Shri @PrakashJavdekar to intervene and send a central team to conduct a detailed investigation into the matter," Rane said in a series of tweets.
"Having a passion for wildlife, especially tigers, this incident in my constituency at Valpoi has taken me by shock. A thorough investigation into the matter is vital.
"It is very important to stop such mishaps as it is our duty to conserve & protect wildlife."
The opposition has lashed out at Chief Minister Sawant.
"Most shocking to hear about murder of Tiger Family by poisoning in Sattari. I condemn the heinous act & demand@goacm to ensure that the killers are caught & given harshest punishment. Let us Live & Let the Tigers Live..," Leader of Opposition Digambar Kamat said in a tweet.
( With inputs from IANS )