Muhammad Ashraf, 56, killed his daughter Saba and her husband Karamat Ali a day after the couple returned to Lahore's Kahna area to smooth over rocky relations with the family, who disapproved of the marriage, according to police.
"18-year-old Saba had married Karamat Ali, who is 35, around a year and a half ago against the will of her family and returned to her home yesterday night to settle matters with father and other family members," Falak Sher, a local police official, told AFP.
"He also killed his neighbour Muhammad Akram for supporting his daughter's marriage," said Sher, adding that Ashraf and his son Safdar later surrendered to police and confessed to the murders.
The incident comes just days after another woman in Lahore, Zeenat Bibi,was set on fire by her mother for marrying a man of her own choice. Bibi's mother later confessed to the crime.
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Earlier today Pakistan's Prime Minister Nawaz Sharif ordered a comprehensive investigation into Bibi's killing, calling the crime un-Islamic.
Hundreds of women are murdered by their relatives in Pakistan each year on the pretext of defending what is seen as family honour.
"A Girl in the River: The Price of Forgiveness" -- a film telling the story of a rare survivor of an attempted honour killing -- won an Oscar for best documentary short in February.
Amid publicity for the film, Sharif vowed to eradicate the "evil" of honour killings but no fresh legislation has been tabled since then.