Russia is blaming the reduced volume of gas deliveries on technical issues resulting from the sanctions imposed by the West over Moscow’s invasion of Ukraine.
The countries said anyone with close ties to Russia or Belarus should also be removed from important sports posts.
Finland had this week applied to join NATO, a move that likely angered Russia.
Ukraine is halting transit of gas through Luhansk, one of its contested eastern regions, gas network operator OGTSU’s data showed on Wednesday.
The deadline for the rouble payments had been set for Thursday. Mr Putin is meeting Gazprom and central bank officials on Thursday.
“Therefore we are not interested in the endless growth of prices for energy resources, including gas,” Mr Putin said on Wednesday.