Traffic arriving at Finland's eastern border with Russia "intensified" overnight, the Finnish Border Guard said on Thursday, while adding that the situation was under control.

Finland is closely monitoring the situation in its neighbour after President Vladimir Putin's order of military mobilisation for the war in Ukraine, Defence Minister Antti Kaikkonen said on Wednesday.

Finnish land border crossings have remained among the few entry points into Europe for Russians after a string of Western countries shut both physical frontiers and their air space to Russian planes in response to Russia's invasion of Ukraine.

"The number clearly has picked up," the Finnish border guard's head of international affairs, Matti Pitkaniitty, told Reuters, adding that the situation was under control and border guards were ready at nine checkpoints.

Putin's announcement, made in an early-morning television address on Wednesday, raised fears that some men of fighting age would not be allowed to leave Russia and prompted one-way flights out of the country to sell out fast.

Finland, which has the longest European Union border - 1,300 km - with Russia, opted to keep its frontier open though has cut back the number of consular appointments available to Russian travellers seeking visas.

Estonia, Latvia, Lithuania and Poland, the other EU countries that border Russian territory, began turning away Russian citizens from crossings at midnight on Monday, saying they should not travel while their country is at war with Ukraine.

The three Baltic nations will offer no refuge to any Russians fleeing Moscow's mobilisation of troops, their ministers said on Wednesday.

Finland is working on its own national solution to limit tourist traffic from Russia, Foreign Minister Pekka Haavisto said during a visit to New York late on Wednesday.

"Finland does not want to be a transit country for (EU) Schengen visas issued by other countries. This is the traffic we want to get under control," Haavisto told journalists.

"The fear is that we will be the only border country through which it is possible to come from Russia to Europe with Schengen visas issued by other countries."

Wednesday's number of people crossing the Finnish border was, however, lower than during the weekend, Pitkaniitty said.

He said 4,824 Russians arrived in Finland via the eastern border on Wednesday, up from the 3,133 a week earlier.

In far northern Norway there had been no changes in the number of Russians crossing into the Nordic country, a police official told Reuters. Norway is not a member of the EU. (Reporting by Stine Jacobsen in Copenhagen, Essi Lehto in Helsinki, Gwladys Fouche in Oslo, Nissi Milla in Gdansk and Andrius Sytas in Vilnius; editing by Terje Solsvik, Kim Coghill and Mark Heinrich)