The families of the Hillsborough victims say the verdicts at the inquest into the deaths of the 96, should be overturned.
Following the three-and-a-half hour meeting, Trevor Hicks from Keighley, who lost his two daughters in the tragedy, gave a statement to the media in which he expressed the Hillsborough Families Support Group's desire for the inquest verdicts to be overturned and new ones to be held in Liverpool.
A statement on behalf of the HFSG, said: "The findings of the Hillsborough Independent Panel have finally vindicated the families in their 23-year struggle to establish the truth.
"However, after truth must come justice. We have spoken today to our lawyers and taken initial advice. As the families have always believed and insisted, it was the actions and inaction of those in authority that caused the deaths at Hillsborough in April 15, 1989.
"The fans did not contribute to the tragedy. Any blame previously laid at their door has been shown to be part of a despicable conspiracy by those in authority to tarnish the reputations of the dead, the survivors of the disaster and the people of Liverpool. This conspiracy has been revealed for what it is; a bid to avoid accountability.
"Those responsible can avoid accountability no longer."
The statement said the families strongly condemn the comments made this week
by West Yorkshire's Chief Constable Sir Norman Bettison, and describes the "monumental" scale of the wrongdoing and cover up that will leave an "indelible stain on the reputations of those authorities in whom the public implicitly placed thier trust."
The HFSG are now looking at three particular avenues to follow up and they are urging the attorney general to apply for new inquests, demanding full and immediate investigations into criminal prosecutions and final, where appropriate, applying for civil proceedings to be reopened.