High Court Judge Brendan Brown said the case can proceed on the condition the family can raise the $20,000 needed for security to cover the costs of a two week trial.
Steven's mother Raewyn told the Herald the family was still deeply affected by Steven's death. Their campaign for justice was amplified by the death of Steven's father, James who had driven the proceedings, last year.
The family set up a donation page tonight.
"James was the one doing it but he passed away last year so we are carrying it on. It's been terrible but people have been so good to us before and we've got to raise the funds to take it to court so we thought we would try Givealittle.
"We have had all these years of trying to get justice because Steven had a right to live."
The family's 16 years battle has cost $150,000.
"We are hoping the good people of New Zealand will once again stand by the family by donating towards our costs, even if it's $1," Steven's sister Kelly wrote on the Givealittle page.
"We are not only fighting for justice for Steven, but for every person out there, so no other family needs to go through this tragedy."
After the shooting, police did not charge Mr Abbott and the decision was backed by the deputy Solicitor General. The Wallace family then took a private murder prosecution against him but a jury acquitted Abbott in 2002, saying that he shot Wallace in self defence.
In September 2014, Steven's father began proceedings against the Commissioner of Police and the Attorney-General under the New Zealand Bill of Rights Act.
He was seeking compensation of $75,000, the amount the family paid for the deposition hearing in the murder trial.
Crown lawyers argued that there had already been the previous legal battles and a Coroner's inquest and Independent Police Conduct Authority report that cleared the officers of all blame.
However, Justice Brown said the case concerned a developing area of the law and the family's submissions presented a different view that should be heard before the courts.