A dozen people were also critically injured in the fire that broke out at about 4 a.m. in Sealdah in central Kolkata when many victims were asleep.
Even as 26 fire tenders battled the leaping flames and firemen scrambled to rescue people, many were feared trapped inside the market that houses shops and paper godowns.
Fire Services Minister Javed Khan said the complex was illegally built during the erstwhile Left Front regime and that most entry and exit gates were locked, trapping people.
Kolkata Mayor Sovon Chatterjee said the fire took a long time to douse as the lanes leading to the market were narrow and dingy.
Locals alleged that the death toll could be more.
The chief minister ordered an enquiry and announced compensation of Rs.2 lakh to the kin of each of the dead and Rs.50,000 to each injured person.
"The probe will be jointly done by police, fire department and municipal corporation. A report is to be submitted in three days.
"On the basis of the report, action will be taken," Banerjee said at the site.
Observing that the market was prone to fire because a large number of inflammable objects were stored, she also hinted at sabotage.
"Why has this incident happened? There are so many inflammable objects that if anybody intentionally lit a small fire, it could turn into a major fire. There can be (a) conspiracy, sabotage. The probe will look into all aspects," she said.
Banerjee visited the injured at the state-run NRS Medical College and Hospital.
"At least 19 people have been killed so far," an officer at the police control room said.
"We will take action against the market authorities for not having any fire safety arrangements," Minister Khan said.
Surjya Kanta Mishra of the Communist Party of India-Marxist demanded a probe.
"This is not the time to play the blame game. An immediate and impartial probe must be initiated and the administration must seriously look into how many buildings there are vulnerable to fire," he said.