With the military offensive ordered last night by Russian President Vladimir Putin, "we have entered a new and dark chapter in European history," Swedish Prime Minister Magdalena Andersson told a press conference.

She condemned "a clear violation of international law and against the European security order".

Despite a debate about NATO membership that has been revived by Ukraine tensions, the Social Democrat leader said Sweden's position on not joining the defence alliance remained in place.

"In a situation like this it is important that Sweden's long-standing security policy stays firm. That we are predictable and clear," Andersson said.

"Sweden has been alliance-free for an extremely long time. It has served Sweden's interests well," she added.

Earlier in neighbouring Finland, the government also ruled out immediate moves closer to NATO membership.

"We have a security policy designed to withstand times of crisis. We will use the means at our disposal, including cooperation with NATO partners," Foreign Minister Pekka Haavisto told a press conference.

"After a crisis, we will see what further action is needed," the minister said.

Finland's President Sauli Niinisto noted that "despite early warnings, this morning has been a shock to us all".

Unlike Sweden, Finland has adopted a so-called "NATO option" provision, which means that "if Finland's security requires it, Finland has the opportunity to apply for membership", Prime Minister Sanna Marin said.

Full membership is an ongoing debate which has already been reignited in recent weeks in Finland, and Russia's action would likely spur a broader debate, Marin noted.

"However, this is a debate that would require broad parliamentary consensus," Marin said.

NATO member Norway condemned a "serious violation of international law" and announced the "temporary" relocation of its embassy from Kyiv to Lviv, in the west of Ukraine.

"The attack is a serious violation of international law and puts innocent people's lives at risk," Norwegian Prime Minister Jonas Gahr Store tweeted.

Denmark, also a NATO nation, summoned the Russian ambassador to condemn the invasion.

"This day is a stain on Russian history. Denmark strongly condemns Russia's ruthless and completely unprovoked attack on Ukraine," Foreign Minister Jeppe Kofod said in a statement.