Thousands of people were caught up in the stampede late Saturday and the victims may have been trampled by the rushing crowd, Budapest police spokeswoman Katalin Fanni Horvath said.
Police and medical investigators were working to determine the cause of the deaths. Police have denied reports that the victims were stabbed.
"Human irresponsibility caused the deaths of the three victims," Interior Minister Sandor Pinter told reporters late Sunday, adding that drugs had been detected in one of the young women.
The incident occurred late Saturday at the West-Balkan nightclub in downtown Budapest, housed on several levels inside a communist-era shopping mall and office complex.
According to district officials, the venue was functioning without a full permit and being allowed to operate only until 10 p.m. with a maximum capacity of 300 people.
An estimated 2,500 people were in the nightclub when the incident occurred just before midnight and 2,881 tickets had been sold, Night Noise Life, the organizing company, said in a message posted Sunday afternoon on its Facebook page. Interior Minister Pinter said 4,000 tickets had been printed.
Family, friends and other mourners lit candles and laid flowers Sunday night outside the nightclub which is across a busy avenue from one of Budapest's main railroad stations.
Prime Minister Viktor Orban and his wife, Aniko Levay, also lit candles at the scene.