More teenagers could have died outside a St Patrick's Day disco where three fatally injured, detectives said.
Eyewitnesses have described chaotic scenes and police confirmed people were trampled underfoot.
Youngsters will not face police action for being under age if they come forward, prosecutors pledged, in a bid to encourage people to tell their stories.
Students Lauren Bullock, 17, Connor Currie, 16, and Morgan Barnard, 17, all from Co Tyrone, died outside the Greenvale Hotel in Cookstown on Sunday night.
Police Service of Northern Ireland (PSNI) Detective Chief Superintendent Raymond Murray said it was fortunate more were not killed following every parent's "worst nightmare".
"Bad enough, a horrendous tragedy, but we could easily have been looking at more," he said.
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.
Officers have traced 160 witnesses and are conducting interviews.
Buses let youngsters off outside the popular nightspot before the disaster happened.
Mr Murray said there was an extended "crush situation" outside one of the doors to the hotel function room.
He praised those in the crowd who worked hard to get party-goers who had fallen down back on their feet when others were falling on top of them.
That created space in the crowd to rescue people.
The senior officer added: "This is an event that should have been a celebration and it has turned into every parent's worst nightmare."
Counselling services are being provided to those affected and prayer services have been held.
Mr Murray said several parents expressed concern that their children, who may have been under age, were trying to enter a licensed premises.
"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."
Books of condolence have opened across Northern Ireland in memory of the three teenagers.
Lauren was a bright and bubbly cheerleader and schoolgirl who lit up the lives of her friends, a close friend said.
Alice Lambert, also 17, from Coalisland in Co Tyrone, was among the first to sign the memorial book in Cookstown.
She said: "She was such a nice person - she was like a ray of sunshine.
"She made you happy, you saw her on a night out and she would have made you happy."
St Patrick's Academy in Dungannon, where the two other victims attended school, said it was a time of "profound sadness".
Morgan was an "ambitious and charismatic" young person with abundant potential.
Teachers said: "He lifted the mood everywhere he went, everyone benefited from Morgan's energetic, positive zest for life. It was contagious.
"His smile was bright and when Morgan was around, fun and laughter always followed."
Connor was a kind-hearted, loyal friend, always willing to help others, "courteous, mannerly and compassionate".
The school said: "He had a great sense of team spirit and his warm, caring nature endeared him to all and earned him much deserved respect."