Victim's family says 'this is true justice' as the four men convicted for gang-rape and murder of 23-year-old receive death sentence

Four men convicted of the gang-rape and murder of a 23-year-old physiotherapist in Delhi last year were sentenced to death on Friday after public calls for them to be hanged.

Bus cleaner Akshay Thakur, gym instructor Vinay Sharma, fruit-seller Pawan Gupta and unemployed Mukesh Singh were convicted this week of rape, unnatural sex, murder, conspiracy and destruction of evidence. They had denied the charges against them.

The sentence was pronounced at 2.30pm by Yogesh Khanna, the judge who has heard the case over seven months at the district court of Saket in south Delhi. Khanna described the attack, on a moving bus on the capital's busy roads on a Sunday evening in December, as having "been committed in an extremely brutal, grotesque, diabolical, revolting and thus dastardly manner" that "shocked the collective conscience".

Officials said three of the four men had broken down sobbing in the police vehicle taking them back to the high security jail where they have been held since being arrested within a week of the crime.

"This is true justice for my sister," Gaurav, the brother of the victim, told the Guardian. The family, he said, were "very happy". His mother embraced senior investigating officers at the courtroom and thanked them. The father of the victim's male friend, who was with her during the attack and was badly injured, welcomed the sentence. "My respect for the Indian judiciary has gone up manifold. It was death they deserved and death they got," Bhanu Pratap Pandey said.

But Ashwini Malhotra, 56, said that he "would still not feel safe sending [his] daughters out on Delhi roads". He told the Guardian: "A lot still needs to be done to make women feel safe in this city. A public hanging would have been great."

Nonetheless, many in India expressed relief that India's criminal justice system, despite its many weakness, had at least functioned in this case. "Finally we can say Indian judiciary works," said Malhotra outside the courtroom, where a crowd cheered as the verdict was announced.

Newspapers said before the sentencing that there was a "strong case for [the] death penalty" and the country's usually argumentative televised debates have struggled to overcome unanimity of opinion on the issue. Sushil Kumar Shinde, the Indian home minister, took the unusual step earlier this week of telling reporters that a death sentence was assured – an indication, observers have suggested, of the government's concern about public anger with the authorities' handling of the case.

The ruling Congress party has been heavily criticised for its slow and insensitive response following the crime.

"There was an atmosphere in the country after this incident … we expected such a punishment," Shinde said on Friday.

The sentence will now be automatically referred to a high court bench of two judges who will consider the sentence and any appeal. If upheld, an appeal to the supreme court is also possible; so too is a pardon from the Indian president, but such a process would probably take years.

Since the trial of the attackers bega≠n in February, one defendant, Ram Singh, has hanged himself in prison, in March. The youngest among the accused, who was 17 at the time of the assault, was tried separately and last month sentenced to three years in a juvenile reform home. Although this is the maximum possible punishment under Indian law, the victim's family have vowed to campaign for a longer sentence.

The horrific assault and murder provoked outrage in India and led to an unprecedented national discussion about sexual violence. The prosecution's case drew on the testimony of 85 witnesses, a statement given by the victim before she died, DNA samples, dental records from bite marks on the victim's body that matched the teeth of some of the men and the evidence of her male friend.

The pair were attacked after boarding the bus on their way home from a movie at an upscale shopping mall and eventually dumped on a roadside layby on the outskirts of Delhi. The woman, whose identity is protected by Indian law, suffered massive internal injuries from repeated penetration with an iron bar and died two weeks later in a Singapore hospital. Her ashes have been scattered in the Ganges near her ancestral village.

Indian laws on sexual assault and harassment have been tightened in the aftermath of the incident but institutional reforms will take much longer, women's rights campaigners say.

Kavita Krishnan of the All India Progressive Women's Association said: "This is not a moment for celebration, though the anger and sense of vindication are understandable. It's a moment to remember the victim and all those other victims who have not received justice."

There have been 1,098 cases of rape reported in Delhi in the first eight months of this year, more than double the number in the same period last year, according to police data.