Finland's Foreign Minister Pekka Haavisto said his country is working with Israel to help Russian Jews leave Russia.
Haavisto said Finland was working on restricting the number of Russians coming into Finland but was helping those most at risk of persecution.
"We want to ensure that Russian Jews, critical journalists and others will be helped to get out," he said on the sidelines of an EU Commission conference on the Baltic Sea region in Lappeenranta, 30 kilometers (19 miles) from the Russian border.
About 66,000 Russians have arrived in the EU in the last week, according to Frontex, the EU's border and coast guard agency. It said the number of arrivals has increased 30% compared to the previous week.
Russian President Vladimir Putin announced a partial mobilization last week.
Frontex estimated that the number of illegal border crossings into the EU is likely to increase if Russia decides to close its borders to conscripts.
On Monday, 7,700 Russians arrived via border crossing points in southeast Finland. Nearly 16,800 people arrived over the weekend via border crossing points in southeast Finland, the Border Guard wrote on Twitter.
A total of 27 people applied for temporary protection and four for asylum. Early Tuesday, a queue of 50 to 70 cars formed at the border crossing.
Unlike the Baltic States and Poland, Finland has not completely restricted the entry of Russian tourists with Schengen visas issued by the EU member states.
On Sept. 1, Finland began restricting the number of tourist visas issued from 1,000 daily to 100.
