Sara Sharif's father and stepmother claim they are willing to co-operate with UK authorities in a video - their first public comments since her death.
The 10-year-old's body was found at her home in Woking, Surrey, on 10 August.
Surrey Police want to speak to her father Urfan Sharif, his wife Beinash Batool and brother Faisal Malik in relation to a murder investigation.
They are known to have travelled to Pakistan from the UK on 9 August and police have been unable to locate them.
In the low-quality footage Mr Sharif does not speak while Ms Batool reads from a notebook.
She spends only two sentences on Sara, describing her death as an "incident".
Ms Batool ends the video saying that they are willing to co-operate with the UK authorities to fight their case.
The BBC was sent the video but has been unable to verify their account. Nor was the BBC able to verify the conditions under which the video was filmed or the location.
In a statement responding to the video, Surrey Police said "clearly this is significant" and it had been working with Interpol, the Foreign Office and the National Crime Agency to work out the next steps.
"As you will appreciate, progressing these enquiries through the appropriate channels has to be handled carefully and sensitively," the force said.
"Any co-operation from the people we want to speak to will assist the enquiry."
An inquest held last month heard the precise cause of death was "not yet ascertained" but was likely to be "unnatural".
Post-mortem tests found Sara sustained "multiple and extensive injuries".
Her mother Olga Sharif told Polish television she hardly recognised Sara in the mortuary because of her injuries.
The majority of the 2 minute and 36 second-long video filmed by Mr Sharif and Ms Batool consists of allegations that the Pakistan police are harassing the couple's extended family, illegally detaining them and raiding their homes.
Ms Batool states that the reason the family are in hiding is because they fear that the Pakistan police will torture and kill them.
In response Jhelum police chief Mehmood Bajwa told the BBC the allegations of harassment and torture of family members are false.
He said if the family had any fears from the police they could go to court to seek protection.
The Pakistan police previously said in court that they have detained some family members for questioning - although they say they were not arrested - and told the BBC that they conducted some raids.
This week they denied in court that they are currently holding certain family members and have told the BBC that they have not tortured or stolen items from the family.
Detectives launched an international search after Sara's body was discovered by police at an address in Woking, on 10 August.
Her father, his partner and his brother, had travelled to Pakistan the previous day.
Sara had been living at the Surrey property with her father, her father's partner, her uncle and five brothers and sisters.
In the interview on Polish television, Olga Sharif said she had separated from Urfan Sharif in 2015. Originally Sara and her older brother had lived with their mother, but in 2019 the family court said they should live with their father, though she still had equal rights.
Police said Mr Sharif, 41, made a 999 call from Pakistan, leading them to find Sara's body, shortly after landing in Islamabad.
Pakistan police say they did not receive a request, via Interpol, to initiate a search for the three until 15 August. Surrey police have not said when they asked Interpol for the search to start.
Pakistan police believe the trio landed in Islamabad international airport early on 10 August.
They believe they travelled to the city of Jhelum and relatives in a small hamlet near Domeli in central Punjab. According to the police investigation the family arrived there, at the home of Mr Sharif's sister and her brother-in-law late at night on 12 August before leaving around 05:00 the following day.
From there police say they do not know where they went.
10 August: Sara's body discovered in Woking. Surrey Police say they begin liaising with international partners. Sara's father Urfan Sharif, his partner Beinash Batool and his brother Faisal Malik arrive at Islamabad and travel to Jhelum
12 August: Urfan Sharif, Beinash Batool and Faisal Malik leave Jhelum late at night to go to Domeli
13 August: The three leave Domeli early morning - the last location confirmed by police
15 August: Pakistan police say they receive request from Interpol via FIA to search for the group
16 August: Pakistan police say they began searching
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