At least one school was evacuated, police questioned two young men about violent Internet postings and a 15-year-old boy was reportedly detained for sending threats to another school.
In neighboring Sweden, police arrested a 16-year-old-boy after viewing a YouTube clip in which he posed with weapons. They also urged residents to report any threatening Internet postings to police.
Finnish police said text message threats were being spread around the western town of Kauhajoki, where a masked gunman killed 10 people and himself in a fiery rampage on Tuesday.
"The text messages are threatening in nature and are causing fear and hysteria among young people," police spokesman Urpo Lintula said. "We must stop them."
He declined to elaborate on the content of messages, but said Finland saw a similar wave of threats after a school shooting at Jokela high school near Helsinki last year.
National Police Commissioner Mikko Paatero said he feared copycat attacks.
"It's clear that the more you talk about these incidents, the more chances there are of copycats," Paatero told reporters in Helsinki. "After we've witnessed two such incidents, the threat is real."
Finnish media said several schools across the nation had received bomb threats. One school with 500 students in the southern town of Keuruu was evacuated due to suspicious text messages and Internet postings, the STT news agency reported.
In the west coast town of Turku, a 15-year-old boy was arrested for sending threatening messages to a school, STT said, while police in the central town of Kajaani detained two men aged 18 and 23 for menacing messages they had posted on the Internet.
"They were fairly vague but they mentioned shootings in schools and bomb explosions," Kajaani police spokesman Arto Lumikari said, adding the men were not believed to be planning any attacks.
Investigators were probing possible links between the Kauhajoki gunman, Matti Saari, 22, and 18-year-old Pekka-Eric Auvinen, who fatally shot eight people and himself at a high school in southern Finland in November.
They said Auvinen and Saari likely bought their guns at the same place and could even have been in contact with each other.
"The cases were similar. They were the same type of person, so it could be possible," investigation leader Jari Neulaniemi told The Associated Press. "They had the same style of hair, same kind of clothing, same interests and ideals - and their deeds were the same."
Both gunmen posted violent clips on YouTube before the shootings, both were fascinated by the 1999 Columbine school shootings in Colorado, both attacked their own schools and both died after shooting themselves in the head.
But Neulaniemi stressed police had not been able to confirm a link between the shooters.
"We have (Saari's) computer in our possession, but the Jokela case was almost a year ago, and we don't yet know how far back the data goes. We haven't examined the computer or the telephone records," he said.
Saari killed eight female students, one male teacher and one male student. A 21-year-old woman that Saari shot in the head is still hospitalized after having two operations.
Sanna Orpana, a Kauhajoki student, said she was in the classroom next door when the shooting started Tuesday at the Kauhajoki School of Hospitality, 180 miles (290 kilometers) northwest of Helsinki.
"We started to hear shooting and a kind of a rumble like tables falling down. We thought someone is playing around, fooling with toy guns," Orpana told AP Television News. "A couple of us went to have a look in the other room through the door. The guy was there with a gun, and tried to shoot them."
She said students hid under a table, then grew frightened that the shooter might come into their room and ran upstairs.
The government pledged to tighten Finland's gun laws and keep mentally unstable people from obtaining firearms after Saari's rampage. Interior Minister Anne Holmlund said a new proposal would give police greater powers to examine gun applicants' health records.
But Finland has deeply held hunting traditions and many homes have guns.
The government has also called for an investigation into police handling of the case. Police questioned Saari on Monday about YouTube clips showing him firing a handgun, but said they found no reason to hold him.
In Sweden, police raided the teen's home in Koping, central Sweden, after seeing the YouTube clip, according to police spokesman Borje Stromberg. They arrested him Wednesday then released him a day later after determining he was not considered a threat.
In a message Thursday on its Web site, Swedish police urged people to report any Internet postings that could be seen as "warning signals of planned crimes."