Police were Tuesday hunting a tribal elder who ordered a teenage couple to be electrocuted by their families as punishment for eloping, in the country's latest gruesome "honour" killing.

The couple, members of the Pashtun ethnic group living in Karachi, fell foul of their families after eloping last month. But police said the man's family persuaded them to return home so they could be married.

A tribal jirga (council) then ordered the couple's execution after the families had put their case to the influential group of elders.

The couple were tied to a wooden bed and electrocuted by family members. Police said the girl was aged 15 or 16 and the man was around 18 years old.

"The (jirga) decided that the girl would be electrocuted by her own father and uncle and the boy by his father and uncle," police officer Amanullah Marwat told AFP, adding that the families later buried the bodies in secret.

Jirgas commonly adjudicate in communal disputes in rural Pakistan, especially in the northern tribal belt, but are rare in cities.

However, the bustling port city of Karachi is home to large numbers of migrants from the tribal territories, where jirgas are held in high esteem.

Police have arrested the relatives behind the killings, charging them with murder and tampering with evidence. However the leader of the jirga who ordered the murders remains at large.

"We are raiding different places to arrest him," Marwat said.

Hundreds of women are murdered by their relatives each year after allegedly bringing shame on their families in the deeply conservative Muslim country.

Under previous legislation the culprits - usually men - could escape punishment if they were pardoned by members of their family.

But in July last year the high-profile murder of social media star Qandeel Baloch, whose brother confessed to the killing, reignited calls for reform.

Parliament has since passed a law aimed at scrapping the ability to forgive "honour" killers. But critics contend some loopholes still exist.