They were arrested on Sunday morning after police were alerted to an ongoing sexual assault by witnesses who reported seeing it live in a closed Facebook group.
Uppsala District Court on Wednesday remanded two of the men, a 20-year-old Afghan national and an 18-year-old, also from Afghanistan, in custody on suspicion of rape.
The third man, a Swedish citizen aged 24 according to court documents seen by The Local, was detained on suspicion of failing to reveal rape.
The men deny the accusations. "I have seen stronger evidence in my days," the 24-year-old's lawyer, Andreas Welin, told Swedish news agency TT after the pre-trial hearing.
"A woman is said to have been raped in an apartment. He is suspected of that," said the 20-year-old's lawyer, Christer Söderberg. "He denies any criminal offence, he has given in my opinion a perfectly coherent story about what happened. I cannot go into details, but he has told me in a way that is not contradicted by anything else," he told TT.
In Sweden, a person suspected of a serious crime can be detained before trial with the approval of a court if there is a risk that they will flee prosecution, obstruct the investigation or continue to commit crimes.
Uppsala's deputy chief prosecutor Magnus Berggren told The Local on Tuesday that investigators have been able to get hold of certain still images and footage, but are still working to find the particular video sequence allegedly showing the rape.
Appeals have been put out for anyone in possession of it to get in touch with authorities.
"In order to get as a clear a picture as possible we are questioning people who have at least seen parts of the live streaming on Facebook," Berggren said.
"A film would of course have been central evidence, but there is also other evidence," he added.
The prosecutor leading the investigation, Pontus Melander, said on Wednesday that they had asked the social media giant for help to retrieve the video.
"Facebook has said that they want to cooperate, but they are based in the US so we need international legal aid, which I have requested," he told TT.