This came hours after the police arrested Atul Singh, brother of a BJP MLA, in connection with the same, as an SIT was formed to probe the incident.
A plea was also moved in the Supreme Court for a CBI probe in the matter.
"The Special Investigation Team (SIT) headed by Additional Director General (ADG) of Police (Lucknow zone) will go into the entire gamut of issues involved in the incident," ADG (Law and Order) Anand Kumar told a press conference here.
A home department spokesman said a case had been registered against Atul Singh under various IPC sections including 302 (murder).
The victim has alleged that she was raped by BJP MLA Kuldeep Singh Sengar and his brothers, and blamed the lawmaker for her father's death.
The BJP MLA, however, has rejected the charges as a "conspiracy" by his opponents.
"The Superintendent of Police (crime branch) will be a member of the SIT, which will look into various aspects of the case, and accordingly take action against those found guilty," he said, adding a woman police officer of DSP rank will also be part of the investigative team.
To a question on the possibility of those close to the lawmaker influencing the case, the ADG said, "The SIT will establish all that...As you know the SHO of the police station and five other policemen have been suspended on grounds of dereliction of duty and mala fide considerations. The entire issue will be reconstructed and whoever is culpable and had tried to shield any person will be taken to task."
Kumar also clarified that the death of the victim's father did not take place in police custody.
"Whatever incident of beating up the deceased took place, it happened in the village. The police in fact admitted him to the hospital immediately. But, whether there has been impartial and proper investigation, all these facts will be probed by the SIT, which will holistically probe the entire issue and the guilty will be booked," he assured.
The victim's father died in custody in Unnaoon Monday, prompting the woman to charge that he was killed inside the district jail at the behest of the BJP MLA.
Opposition stages protest:
Meanwhile, opposition Samajwadi Party workers on Tuesday staged a demonstration in Hazratganj area in the heart of the state capital demanding immediate arrest of the BJP MLA.
A five-member women's fact-finding team has been constituted by the party to visit Unnao, SP spokesperson Rajendra Chaudhary said.