Few details of the plots have been revealed, but the chief operating officer of the Security Service confirmed to the Aftonbladet newspaper that its officials had been investigating the potential crimes.
Anders Kassman said that the attacks were discovered following research and intelligence gathering by the security agency. Both foiled plans were intended to be carried out inside Sweden.
He did not reveal if the suspects were intending to carry out suicide bombings.
"We are talking about terrorist acts. That alone makes it serious," he told the magazine.
Sweden was rocked by a suicide attack in 2010, when a man blew himself up on a popular shopping street in central Stockholm. Only the bomber died.
Foreign Minister Carl Bildt said at the time that the "attempted terrorist attack" could have been "truly catastrophic".