Nineteen-year-old Seamus Bradley was shot dead by a British soldier during a military operation in Derry in 1972, called Operation Motorman.
Earlier this year a coroner ruled that the use of force was entirely disproportionate to any perceived threat.
Lawyers for the MoD are now seeking to judicially review the outcome in a bid to secure a fresh inquest.
The High Court was told today that it involves a challenge to the coroner’s finding of facts.
It will also be contended that insufficient reasoning for the decision was given.
Setting aside two days for the case, Mr Justice McAlinden pledged: “I will try and get it on before the end of February.”
Mr Bradley was killed in the Creggan area of the city on July 31, 1972 at the start of Operation Motorman – an Army attempt to gain control of no-go zones for security forces at the height of the Troubles.
The shooting, by a soldier from the Royal Scots Regiment, has been a matter of intense dispute ever since.
The Army claimed he was shot while he was in a tree and suffered additional injuries as he fell.
But his family insisted the killing occurred later, claiming he was taken away in a military vehicle and sustained fatal injuries while being interrogated.
Both versions of events were rejected in inquest findings delivered in August.Coroner Judge Patrick Kinney held that Mr Bradley was killed by a soldier who got out of a Saracen vehicle, dropped to one knee and fired a number of shots.
He said the deceased was running across open ground and clearly had no weapon.
At the time of the shooting there was no other immediate or apparent threat to the soldiers in that area.
Judge Kinney concluded that the use of force by the soldier who opened fire was not justified.
He also ruled that the investigation into Mr Bradley’s death was flawed and inadequate.
Those determinations are now set to be contested at the High Court.
Counsel for the coroner confirmed the scope of the judicial review proceedings.
Fiona Doherty QC said: “There are challenges to the coroner’s findings of fact.”
The case has been adjourned until the New Year.