The three men included forest guard Vijay Bamania, an official trained to shoot tranquiliser darts, and a veterinary doctor.
Shrivastava said that the cage was "well locked" and that the men were in minimal danger, adding the cage was usually used to trap monkeys.
He told the Indian Express: "Initially we placed goats inside as bait, but it did not work. Now the men sit inside the cage, which is well-locked. (They) are supposed to alert others if they sight the leopard."
The latest victim was identified as Mathuri Ganava, who went into the forest on the morning of November 28 around 7am to get firewood with three other women. This was the third death due to attack by the same leopard within a week in the Dhanpur disrict.
The leopard attacked Ganava and dragged her into the bushes, but the other women escaped, the Times of India reported. Villagers later found Ganava's body, saying that her head had been torn from her body.
"The killing was most brutal. Besides placing the cage, we are now planning ways to nab the leopard", said J L Zala, deputy conservator of forests for the region.
The two previous victims were, two village girls that were in the woods helping to tend their families' cattle, Ashwinta Pasaya, nine, and eleven-year-old Jyotsna Parmar.
Bamania, the forest guard in the cage, said he saw it as "part of my duty to protect human lives". He added: "Our prime objective is to catch the leopard and stop loss of human lives.
"We were not scared at all. We spent four hours in the cage on Friday, from 6 to 10pm. We had a torch, while a goat was tied in the open nearby. We also had a machine to make goat sounds to attract the leopard. Around our position we scattered dried leaves so we could hear the leopard coming."
Forestry rangers said the first attempt would be to trap the leopard, but they may have to try and tranquilise it or - as a last resort - kill it.
This article originally appeared on the Daily Telegraph.