A fire brigade spokesman said 35 fire engines were battling the fire, which was now under control.
"We can confirm 18 deaths, but the unofficial toll is higher," the spokesman said. "A long cluster along the river was affected. It could be around one kilometre or more."
The blaze affected more than 1,000 huts in the Vijay Ghat area near the Yamuna river. The fire brigade found it difficult to move vehicles through the district's narrow lanes.
Indian news reports said 26 people died in the slum quarter, where there are about 50,000 huts. They quoted police as saying most of the bodies were found in a mosque.
Witnesses at a hospital said they counted 17 bodies. They also said people threw stones and damaged fire engines because they arrived long after the fire started in the slum, which is populated by rag-pickers and poor people who trade in junk and old newspapers.
"They came more than two hours after the fire started. Many huts could have been saved," one resident said.
The cause of the fire was not known, but some witnesses said they heard a loud cylinder blast which might have started it. Left-wing politicians in the city blamed sabotage by right-wing opponents.
The blaze broke out shortly before the start of a public meeting against a campaign to evict the slum-dwellers because they were illegal immigrants from Bangladesh.
The Communist politicians Hannan Mollah and Nilotpal Basu said: "We have strong reasons to believe that the fire might not be accidental as the spirit of the people galvanised by the meeting could have been a provocation for the vested interests, who would like to have these poor people out of the area."Reuse content