STOCKHOLM (Reuters) -Sweden's national security service raised its terrorist alert to the second-highest level on Thursday and warned that the threat of attack could persist for a long time after burnings and other acts against the Koran outraged Muslims.

Denmark and Sweden have tightened border controls as authorities in both countries fear revenge attacks after anti-Islam activists burned and damaged several copies of the Muslim holy book in recent months.

Sweden's SAPO security service raised the warning level to 4 from 3 on a scale that runs from 1 to 5, reflecting a "high threat".

"Sweden has gone from being considered a legitimate target for terrorist attacks to being considered a prioritised target," head of SAPO Charlotte von Essen told a news conference.

She also said the attack threat posed by "violent Islamist actors" has increased in the past year.

Britain and the United States have warned nationals against going to Sweden due to possible terrorist attacks amid protests there and in neighbouring Denmark over the Koran burnings.

Sweden and Denmark are among the most liberal countries in the world, and have long allowed trenchant criticism of religions.

But Muslims view desecrating the Koran, which they consider to be the literal word of God, as a grave offence worthy of severe punishment.

Sweden's biggest terrorist attack in recent history occurred in 2017, when an Uzbek immigrant who had pledged allegiance to the Islamic State mowed down pedestrians on a busy Stockholm street with a truck, killing five people.

(Reporting by Simon Johnson, Johan Ahlander Terje Solsvik, Louise Rasmussen and Niklas Pollard;Editing by Andrew Cawthorne and Devika Syamnath)