Eight members of the Cuban national men's volleyball team, including the team's captain, are being held in Tampere on suspicion of aggravated rape.
The Central Finland Police Department says that three of the men were detained on Saturday morning and a fourth was taken into custody on Sunday morning. Four more were taken into custody on Sunday afternoon after the team's match against Portugal.
Police said on Sunday afternoon that progress has been made in the investigation.
The suspected incident took place in the Tampere hotel where the Olympics-bound Cuban team is staying.
Inspector Joni Länsipuro of the Central Finland Police Department, who is heading the investigation, told Yle on Sunday that there is one alleged victim in the case, who has been interviewed.
He added that a decision on placing the men who were held on Saturday under formal arrest must be made by noon on Tuesday, 5 July.
"I have not made this decision yet," said Länsipuro. "When the prosecutor comes to work on Monday, we'll discuss this."
Later he added: "It is quite natural that they most likely will not be able to leave Finland on Monday as planned."
Police have refused to reveal more details of the case.
Saturday's detentions took place before Cuba's game against Finland. Three members of the team, aged 19 to 21, were missing from the line-up.
The host team recovered from a loss on Friday to beat Cuba in four sets, 3-1. On Sunday, Cuba arrived for a match against Portugal without their captain.
Länsipuro says that normally police do not make statements about such cases at such an early stage. They decided to in this instance because of speculation that the players had defected or otherwise gone missing.
Tampere is hosting qualifications for the FIVB Volleyball World League Finals. The Cuban team is scheduled to play in the Rio Summer Olympics, which begin on 5 August.
7:04 pm: Updated number of detainees and Länsipuro's comments.