Two policemen were also injured, he said.
The four men were arrested on November 29 for allegedly raping and killing the woman by smothering her and later burning her body, an incident that led to widespread outrage and recalled the horrors of the December 16, 2012 gangrape and murder of a physiotherapy intern in Delhi.
They were remanded to seven days' judicial custody.
News of the 'encounter' killing led to celebrations in some quarters and concern in others.
The father and the sister of the woman veterinarian said they were very happy and thanked the Telangana government and police.
"We watched on TV that they were killed in an encounter. We are very happy. Even people are happy. I thank the Telangana government and police for the encounter. I thank everyone who stood by us," the father told the media.
The young woman's sister hoped the killings would be a deterrent for others.
"With this incident people should be scared to commit such crimes (against women)," she said.
While the woman veterinarian has come to be known as "Disha", direction, the Delhi girl was dubbed "Nirbhaya", the fearless one.
Seven years after their daughter was gangraped -- she died in a Singapore hospital a fortnight later -- Nirbhaya's parents also expressed satisfaction and the hope that their daughter's culprits would be hanged soon and justice would be theirs.
Nirbhaya's mother appealed to authorities to not punish the policemen involved in the encounter.
"The family of the Hyderabad doctor will not have to wait for justice for seven years like us. Police did the right thing," her father told journalists.
There were celebratory scenes at the 'encounter' site as well with scores of people gathering to congratulate the police and shouting slogans such as "Telangana Police zindabad" . Some women were seen distributing sweets to police personnel.
Many political leaders stepped into the growing debate.
Samajwadi Party MP Jaya Bachchan, who had recently advocated lynching of rapists in Parliament, said the killing of the four men was "long due".
"Better late than never," she said.
BSP president Mayawati also praised the police for its strong action against the accused.
But there were others who expressed their consternation.
Congress leader and Lok Sabha member Shashi Tharoor said extrajudicial killings were not acceptable.
"We need to know more... Until details emerge we should not rush to condemn. But extrajudicial killings are otherwise unacceptable in a society of laws," he tweeted.
BJP leader Maneka Gandhi slammed the police and said it set a "horrifying" precedent.
"Jo bhi hua hai bohot bhayanak hua hai is desh ke liye (What happened was horrifying for the country)... You cannot kill people because you want to. You cannot take law in your hands, they (accused) would have been hanged by court anyhow," the former minister said.
Rekha Sharma, National Commission for Women chief, said she was happy the perpetrators were dead, but justice should have been done through proper legal channels.
Several rights activists spoke out to express their outrage and said the police cannot act like a lynch mob under any circumstance.
The encounter is an attempt by authorities to distract people from the government's failures to safeguard women's rights, the activists said, calling for an exhaustive inquiry.
According to Kavita Krishnan, secretary of the All India Progressive Women's Association, the killing of the four men is not justice but a "ploy" to shut down demands for accountability from the police, judiciary, governments, and justice and dignity for women.
She described the incident as the admittance of utter incompetence and failure of criminality on the part of the entire political and police system and accused Telangana Chief Minister K Chandrashekar Rao of deflecting the "whole issue".
Krishnan said the police personnel responsible must be arrested and prosecuted, and must be asked to prove in court that all four men were killed.
"It was an attempt to divert attention from the issue. A high level inquiry in the matter is needed," said Annie Raja, general secretary of the National Federation of Indian Woman (NFIW).
Lawyer and rights activist Vrinda Grover termed the incident "absolutely unacceptable".
Asking people to say "no to trigger track injustice", she said, "... so all that the state will do in the name of ensuring that women live as equal and free citizens is to add to its arsenal of unlimited, arbitrary violence."
She also asked for an independent judicial inquiry into the incident.
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