Mumtaz Sattar, 38, from Port Glasgow, Inverclyde, died in Pakistan shortly after arriving in the country last month.
Her relatives have lodged a petition at the High Court in Lahore which names a single murder suspect, who cannot yet be identified for legal reasons.
The case was discussed at a meeting in Scotland yesterday involving the new governor of the Punjab region, former Glasgow Labour MP Mohammad Sarwar, plus Mumtaz Sattar's brother, Sarfraz Ali, and Glasgow-based solicitor Aamer Anwar, the family's lawyer.
Anwar said Sarwar gave assurances during the meeting that justice would be done, after the family aired concerns about the investigation.
He added: "The serious concerns of the family were raised with regards to the police investigation and Mr Sarwar assured us that justice would be done.
"A conference call then took place with senior police officers in Punjab, the governor and myself."
First Minister Alex Salmond also discussed the case with Sarwar during an earlier exchange this week.