The arrests come amid growing concern in Western capitals about their countries' citizens joining fighters in Syria and then returning to Europe to launch terror plots in their home country.
When asked whether Finland faced threat from terrorism, the country's President Sauli Niinisto said: "Fortunately, actually, none".
At the same time he hastened to add that 40 of his countrymen are supposed to have gone to war-torn Syria to fight with the dreaded Islamic State militants.
He said authorities were already discussing what would be the impact of when some of these people returned to Finland after fighting in Syria.
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"Terrorism is not a concrete problem for Finland but surely, we all the time think how to maintain the situation so that it would not become a concrete problem," he said.
Niinisto, who had addressed the UN General Assembly last month in New York had said that "The war in Syria has severely affected the security situation in the whole region: the geographical expansion of the ISIL organisation, with its horrendous terror, is a by-product of the conflict.
"Finland will contribute to these common efforts," he had said.
US officials have warned that the volume of foreign fighters in Syria raises the stakes for all concerned, as many of those fighters can slip across the border into Turkey and reach Europe with ease.
British police arrested four people in London last week as part of a probe into Islamist extremism.
Police in Australia last month carried out raids in two major cities, including Sydney, in a raid aimed at disrupting what they said were plans by local supporters of Islamic State to behead members of the public.