Finland's president Sauli Niinistö said on Tuesday that the Minsk process, which aimed to provide autonomy for some regions of Ukraine while stopping short of granting them independence, is now dead.
Niinistö said that it was difficult to predict what might happen next.
"The crisis is no longer a European crisis, the UN's Security Council has discussed the issue," said Niinistö. "Russia did not receive support, but got significant criticism."
"If Russia expands its operations, we will end up with [EU-Russia] relations colder than during the Cold War, and for a long time too," said Niinistö.
Russian President Vladmir Putin had announced on Monday that Russia will now recognise the independence of the two regions, which are centred on Donetsk and Luhansk in the east of Ukraine.
Putin also ordered Russian troops to move into the two regions.
Finland has said that its position as a non-Nato member could be reconsidered in light of the international security situation, if necessary.
"I think that everyone is pondering that," said Niinistö.
Niinistö said he had discussed current security policy and possible applications for Nato membership with the leadership of each of Finland's nine parliamentary parties on Monday, as well as with members of the government at a Foreign and Security policy committee meeting on Tuesday.
Niinistö said that while Finland did not face a military threat at the moment, and the security situation in the Baltic Sea remained calm, Russia's actions would have an impact on Finnish-Russian relations.
"Of course this has an effect on how Russia is dealt with," said Niinistö. "There are no concrete changes on the horizon, however."
The president added that Finland strongly supported 'Ukraine and its people'. Finland's own position remains unchanged.
"Finland is a stable democracy, an EU member state, and that picture isn't affected by these events," said Niinistö.
He rejected the idea that Putin's reference to Vladimir Lenin, who granted Finnish independence in 1917, had any impact on Finland. Putin had said that Lenin was wrong to encourage nations in the Russian empire to pursue independence.
"It raised the thought that Finland wasn't even mentioned," said Niinistö. "We would do well to remind ourselves that this doesn't necessarily apply to us."
Finland's parliament was due to debate Russia's moves on Tuesday afternoon, with Prime Minister Sanna Marin (SDP) set to address MPs on Wednesday.
There has been some pressure on Finland to adjust its stance opposing arms exports to Ukraine.
Last week's APN podcast discussed the uncomfortable history surrounding the term 'Finlandisation'. You can listen to the full podcast using the embedded player here, via Yle Areena, Spotify, Apple Podcasts or wherever you get your podcasts.