Police and prosecutors made the pledge in an effort to get more teenagers to come forward to speak to officers about the tragedy.
Schoolchildren Lauren Bullock, 17, Connor Currie, 16, and Morgan Barnard, 17, all from Co Tyrone, died in the incident outside the Greenvale Hotel in Cookstown on Sunday night.
Giving an update on the police investigation, Police Service of Northern Ireland (PSNI) Detective Chief Superintendent Raymond Murray said it was fortunate more were not killed in the crush.
“We could absolutely have been looking at more,” he said.
Books of condolence have opened across Northern Ireland in memory of the three teenagers who died.
Mr Murray said CCTV footage indicated that between 350 to 400 people had either been in the queue or the nearby area when the incident unfolded.
He said officers have traced the identities of 160 witnesses and already spoken to a number of them.
Mr Murray urged more young people to come forward, insisting that in the circumstances police were not concerned whether they were underage and attempting to enter a licensed premises.
He said he had received the same assurance from Northern Ireland’s Director of Public Prosecutions Stephen Herron.
“I want to thank everyone who has spoken with us so far, however there is still a significant number of people who were there that night, in the queue, and I need them to come forward to speak to police so we can understand what happened,” said Mr Murray.
“A number of parents have indicated they are concerned that their children, who may have been underage, were trying to enter a licensed premises,” he said.
“I want to reassure you, the focus of our investigation is not the age of people who were at the event - it is about trying to find answers for the families of the three teenagers who tragically died - we need to know what you saw so the heartbroken families of Connor, Lauren and Morgan know what happened to their children.
“I would urge parents to talk with your children, support them and encourage them to come forward and tell their story to police so we can get an accurate picture of events that night.
“Talk to your children, reassure them - we know they may be scared - but again I can assure you we are only interested in establishing what happened.
“Their account of events on Sunday night could be crucial to establishing how Connor, Lauren and Morgan died.”