Online social networks erupted with outrage over the video posted on Wednesday featuring the girl naked on a bed and the apparent rapists bragging that she had been raped by more than 30 men.
They are suspected of assaulting her on May 21 in Rio de Janeiro, a city stricken by violent crime and which will host the Olympic Games in August.
The authorities have promised to bring the men to justice.
“Those who committed this heinous crime will be found, will be imprisoned and condemned,” Justice Minister Alexandre de Morais told a news conference in Rio Friday night.
Police have identified four of the men suspected of taking a “direct or indirect” part in the rape or the posting of the video, Rio police chief Fernando Veloso told reporters.
“We cannot say whether there were 30 attackers, 33 or 36. The investigations will determine that,” he said.
Brazil’s acting president Michel Temer and other senior figures reacted with outrage.
“I condemn most forcefully the rape of the teenager in Rio de Janeiro,” he wrote on Twitter.
“It is absurd that in the 21st century we should have to live with barbaric crimes such as this.”
The authorities are working “to find those responsible and rigorously punish the authors of this rape and the publishing of this criminal act on social networks,” he said.