Two people have been detained by Rajkot police in connection with the fire that killed at least 33 people, including nine children, Indian media reported.
The blaze broke out at an entertainment complex in Rajkot, Gujarat state, on Saturday.
Gujarat chief minster Bhupendra Patel promised strict action against anyone found responsible when he visited the site on Sunday morning.
More than 300 people were in the two-storey building at the TRP gaming zone and theme park, Rajkot fire officer Ilesh Kher said.
“People got trapped as a temporary structure at the facility collapsed near the entrance, making it difficult for the people to come out,” he said.
District police commissioner Raju Bhargava said the fire was under control and the rescue operation and mission to recover bodies was under way.
“The gaming zone is owned by a person called Yuvraj Singh Solanki," Mr Bhargava said.
"We will be registering an offence for negligence and the deaths which have occurred. Further investigation will take place once we complete the rescue operation."
A police official at the local hospital said some of the bodies were charred beyond recognition.
India's Prime Minister Narendra Modi wrote on X that he was “extremely distressed by the fire … My thoughts are with all those who have lost their loved ones. Prayers for the injured.”
The park was packed with families with children enjoying the school summer holiday.
Footage showed firefighters clearing debris around collapsed tin-roof structures that media reports said were used for bowling, go-carting and trampoline attractions.
Babies killed in blaze at Delhi hospital
Fires are common in India, where builders and residents often flout construction laws and safety codes.
In the capital New Delhi, six newborns died in a fire at a baby care hospital, local authorities said on Sunday.
TV footage showed firefighters attempting to douse the blaze, which broke out late on Saturday night and engulfed the hospital in the eastern part of the city.
The owner of the baby hospital has fled, Delhi police said.
"The causes of the incident are being investigated and whoever is responsible for this negligence will not be spared," Delhi's Chief Minister Arvind Kejriwal said in a post on X.
