NIO Minister Hugo Swire has said he plans to arrange a meeting between the family of Majella O'Hare and Secretary of State Owen Paterson
The meeting is to discuss the Historical Enquiries Team's report into her death.
The 12-year-old schoolgirl was shot by a soldier near her County Armagh home in 1976. Last week, the HET backed the original police investigation.
SDLP MLA Dominic Bradley said the report contradicted the Army's story.
"The soldier and the Parachute Regiment maintained there was a gunman present in the area on that day and that he had fired shots at them and that the soldier had returned fire.
"But as the HET report clearly shows that was not the case," Mr Bradley said.
"So the truth of Majella's death needs to be acknowledged by the British government."
Majella, from Whitecross, was on her way to church on 14 August, 1976, when she was hit in the back by a bullet.
Private Michael Williams was charged with manslaughter after an RUC investigation, but was acquitted in court.
Last Thursday, the HET said it had sent a letter to Majella's mother, regarding its findings and that the final copy of its report would be sent to her in "four to six weeks".
An HET spokesman added: "The original RUC investigation found that Private Michael Williams was not returning fire at a gunman as he claimed and they recommended to prosecutors that he be charged with manslaughter.
"The prosecutors agreed and charged him with manslaughter, but he was acquitted.
"The HET supports the findings of the original investigation. We also said the RUC investigation was thorough and good."