A compensation of Rs 1.5 lakh has also been announced for the victim's family, officials said.
Kiran was playing when the gate fell on her, the police said adding that the child was rushed to a hospital where she died while undergoing treatment.
Following the incident, the UP Rajkiya Nirman Nigam (UPRNN) has constituted a two-member committee to probe the happening and submit its report within a week.
The UPRNN also announced a compensation of Rs 1.5 lakh for the kin of the victim, who would be cremated at her native place in Lakhimpur, officials said.
The 'Lok Bhawan' building houses the chief minister's office where cabinet and other meetings are held.
A portion of this building is under construction. The construction work had started in the Lok Bhawan building during the previous government's tenure, officials said.