Subash Chand Tomar, 47, was rushed to hospital on Tuesday where he died after reportedly being beaten by protesters.
"It was the result of him performing his duty," says police officer Taj Hassan.
"We took our positions that evening during the protest, when fires were burning and tear gas was being fired."
Mr Tomar's funeral included a gun salute from a guard of honour and he was farewelled as authorities closed roads in the centre of the city in an attempt to put an end to a week of demonstrations.
Police say they have charged eight people over his murder.
A spokesman for the Delhi police, Rajan Bhagat, has echoed the prime minister's call for calm.
"This is an appeal to all the demonstrators that peace should be maintained," he said.
"It is their moral right. However, if they indulge in violence, then such incidents cannot be avoided.
"One of our very good constables lost his life and we pay tribute to him."
But demonstrations continue, despite the government's promise to consider demands the six attackers arrested face the death penalty.
Authorities have sealed off parts of New Delhi, but about a kilometre from parliament, demonstrators gathered including documentary film maker Meha Mishra.
"Our fight is against the Indian government, the Indian police, who are not taking any action against this brutal thing which is happening almost every day in our country," she said.
The protestors plan to send a petition to the prime minister to ensure he knows people across the country are concerned about the safety of women
A doctor at the city's Safdarjung Hospital says the rape victim is recovering from her injuries.
"She is conscious. She is alert. She is communicating, by gestures," said the un-named doctor.
He says her ventilator support has been drastically reduced but she is still unable to breathe on her own.
"That is a slight concern, though she is better than before," he said.