Three teenage girls have been buried alive by their tribe in a remote part of Pakistan to punish them for attempting to choose their own husbands, in an "honour" killing case.

After news of the deaths emerged, male politicians from their province, Baluchistan, defended the killings in parliament, claiming the practice was part of "our tribal custom".

The girls, thought to have been aged between 16 and 18, were kidnapped by a group of men from their Umrani tribe.

They were driven to a rural area and then injured by being shot. Then, while still alive, they were dragged bleeding to a pit, where they were covered with earth and stones, according to the findings of Human Rights Watch, the international campaigning group. Officials, speaking off the record, confirmed the killings.

However, six weeks after the deaths, no one has been arrested, amid claims of a cover-up. According to several accounts, Baluchistan government vehicles were used to abduct the girls, and the killing was overseen by a tribal chief who is the brother of a provincial minister from the ruling Pakistan People's party.

Some reports said that two older relatives of the girls had tried to intervene, but they too were shot and buried with the girls while still alive. "This is a heinous criminal offence," said Ali Dayan Hasan, of Human Rights Watch. "We have corroborated it and cross-corroborated it, but the second the police admit that it happened, it would trigger an investigation."

Hasan said that, with a presidential election on September 6, one in which Baluchistan's provincial parliament would be strongly relied on to deliver votes, action that would antagonise the region's politicians was highly unlikely.

In Pakistan's national parliament, an MP from Baluchistan, Israrullah Zehri, said on Friday that "this action was carried out according to tribal traditions", a view backed up by some other male lawmakers, who attacked a woman senator who had raised the case.

"These are centuries-old traditions and I will continue to defend them," Zehri added over the weekend.

The killings happened in the Naseerabad district of Baluchistan. Although so-called honour killings are not unusual, burying the victims alive seems to have been brutal even by tribal standards.

"It is very common for women in these cases to be deprived of an honourable burial. This is to make sure others learn the lesson," said Samar Minallah, a human rights activist based in Islamabad.

Sarang Mastoi, a local journalist in Baluchistan with Pakistan channel KTN, said that the villagers were scared to talk openly about the crime, but he had been taken by some to see the burial site.

Under tribal - not religious - tradition, marriages are carefully arranged by elders. Marrying without permission is considered an affront to the honour of the tribe. Sadiq Umrani, a provincial minister, has admitted that the girls were buried alive but denied the involvement of his brother.

An editorial, published in Pakistani daily The News yesterday, said: "Surely the government should be seeking the murderers, not protect [them] through some dark conspiracy of silence. The fact the act was 'kept quiet' means the government sympathises with such doings."