HELSINKI (Reuters) - Finland said on Tuesday a sharp rise in the number of asylum seekers had increased the threat of terrorism in the Nordic country, with the risk level raised to "low" from "very low".

The Finnish Security Intelligence Service (FSIS) said it was monitoring some 300 people for possible connections to Islamist militant groups, some of whom were among 25,000 asylum seekers to have arrived in Finland so far this year.

Militant groups that seek to recruit people now have a presence in Finland, the FSIS added in a statement.

The terrorism threat level has been raised from "very low" to "low", FSFS director Antti Pelttari told national broadcaster YLE. "The sudden change in the refugee situation means a significant threat to Finland's security."

About 700,000 refugees and migrants have poured into the European Union from war-torn and deprived areas of the Middle East, Africa and Asia in 2015, causing major financial strain on EU member countries, political disputes within them over to how to best handle the influx, and heightened security concerns.

The FSIS said 15 people who recently left Finland to join militant groups in armed conflicts abroad, mainly in Syria, had been killed, while 20 had returned to the Nordic country.

At the same time, the FSIS said, the rapid growth in the number of refugees had created an anti-immigrant atmosphere where the threat of violent hate crime had also increased.

Dozens of anti-immigrant demonstrations have taken place in Finland since late summer, and on Saturday, a petrol bomb was thrown into a center housing underage asylum seekers.

"Finnish extremist organizations have been activated to oppose immigration, and this is the most visible and concrete security threat," Interior Minister Petteri Orpo told YLE.

Finland expects 30,000-35,000 asylum seekers to arrive this year, compared with 3,600 in 2014.

(Reporting by Anna Ercanbrack; Editing by Jussi Rosendahl and Mark Heinrich)