Eight members of the same family were killed after petrol bombs were thrown through the windows of their home in Birkby, Huddersfield, in 2002, in the name of 'family honour'.
Prime suspect Shahid Mohammed, who had skipped bail and was the subject of a huge manhunt for 12 years, was arrested in Pakistan more than three years ago.
But with no extradition treaty in place between the UK and Pakistan, the process of asking for him to be brought back to face a British court has been beset by delays.
The Home Office has now confirmed to The Yorkshire Post that an appeal by Mohammed against extradition has been rejected by the Pakistani courts, although the legal process of bringing him to the UK is still expected to take some time. He remains in custody in a jail in Pakistan.
Detective Superintendent Nick Wallen, who has been leading the investigation, said: “We welcome this development in this ongoing investigation.
“We will continue to liaise with the Home Office and Pakistani authorities throughout the next steps of the process.”
The Chisti family tragedy remains the biggest single event of multiple murders that West Yorkshire Police has investigated in nearly 30 years.
The fire killed Nafeesa Aziz, 35, and her daughters Tayyaba Bootall, three, Rabiah Bootall, 10, Ateeqa Nawaz, five, Aneesa Nawaz, two, and Najeebah Nawaz, six months.
Miss Aziz’s brother, Mohammed Ateeq-ur-Rehman, 18, also died in the fire, and their mother, Zaib-un-Nisa, 54, died a week later in hospital.
In July 2003, three Huddersfield men - Shaied Iqbal, Shakiel Shazad Amir and Nazar Hussain - were convicted for their part in the crime.
Huddersfield MP Barry Sheerman has been lobbying Government ministers to persuade the Pakistani authorities to extradite Mohammed.
He praised the work of the police and other authorities in getting to this point in what he described as one of the most serious and longest-running murder cases he had dealt with in his 40 years in Parliament.
But he struck a note of caution, saying: “All we want is justice for the family and we have had a lot of false dawns. We often thought we were nearly there. We will just quietly keep on persisting.”
Surviving members of the Chisti family marked the 16th anniversary of the fire in May.
Muhammad Shafique, who had escaped the fire by jumping out of a window but lost his mother, brother, sister and five nieces, spoke at the time of his family's frustration at the length of time the extradition request was taking but said they just had “to be patient”.
He said: “It is frustrating. We are very concerned that it has been three years and he is still in custody over there.”