"The investigation remains open until the facts are fully clarified. Further arrests are not ruled out in the coming hours," the national police service tweeted.
The 24-year-old nursing assistant was killed in the early hours of Saturday outside a nightclub.
A witness who was interviewed on La Sexta television said one of the assailants shouted homophobic slurs during the attack.
Protesters took to the streets of Spain's main cities on Monday night to vent their fury at the killing and to demand better protection for gay rights.
Riot police in Madrid baton-charged some demonstrators, prompting the government to open an investigation into their conduct.
Government spokeswoman Maria Jesus Montero said it was important to highlight Spanish society's rejection of the crime but the police were justified in their response to restore order.
Earlier on Tuesday the cabinet approved a bill to tighten up sexual-assault laws and define all non-consensual sex as rape as part of a broader push to legislate against historically macho attitudes.