Kremlin spokesman Dmitry Peskov told reporters that “the alliance remains a tool geared towards confrontation”.
It comes as US defence officials said Moscow’s invasion of Ukraine has been a “massive strategic blunder” which is likely to bring Nato enlargement.
US officials expect the Nordic neighbours to bid for membership of the alliance, potentially as early as June.
Washington is believed to support the move which would see the Western alliance grow to 32 members. US State Department officials said last week that discussions had taken place between Nato leaders and foreign ministers from Helsinki and Stockholm.
Before it launched its invasion, Russia demanded that the alliance agree to halt any future enlargement, but the war has led to the deployment of more Nato troops on its eastern flank and a rise in public support for Swedish and Finnish membership.
Finnish MPs are expected to receive a security report from intelligence officials this week, and Prime Minister Sanna Marin said she expects her government “will end the discussion before midsummer” on whether to make a membership application.
And Sweden’s ruling Social Democratic party, which has traditionally opposed Nato membership, said it is rethinking this position in light of Russia’s attack on its western neighbour. Party secretary Tobias Baudin told local media that the Nato review should be complete within the next few months.
“When Russia invaded Ukraine, Sweden’s security position changed fundamentally,” the party said in a statement on Monday.
But Moscow has been clear that it opposes any potential enlargement of the alliance. Mr Peskov warned the bloc “is not that kind of alliance which ensures peace and stability, and its further expansion will not bring additional security to the European continent”.
Last week Mr Peskov said that Russia would have to “rebalance the situation” with its own measures were Sweden and Finland to join Nato.
Nato was formed in 1949 to counter the threat of Soviet expansion, though since the fall of the Berlin wall a number of formerly communist eastern European countries have joined.
Member states agree to come to one another’s aid in the event of an armed attack against any individual member state.
Despite the threats, both countries have pushed ahead with their bids and stepped up defence spending.
On Monday, army leaders in Helsinki announced a new plan to allocate €14m (£10.88m) to purchase drones for Finland’s military.
And last month Swedish officials said they would boost defence spending by three billion kronas ($317m; £243m) in 2022.
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