On Wednesday afternoon, Nato confirmed to SVT Television News that the warships had entered the Baltic Sea.
"We can confirm that two Russian warships have newly arrived in the Baltic Sea," Dylan White, spokesperson at nato headquarters in Brussels told SVT.
The two unarmed vessels, which are equipped with the Kalibr long range missile system and can be fitted with conventional or nuclear warheads, e passed through the Black Sea and the Mediterranean and by Wednesday morning had passed through the Danish Straits heading for the Baltic.
"It is not conducive to relaxation," Peter Hultqvist (S) said to news agency TT.
But Sweden has an eye on the situation, according to the Minister.
"We have information and are following developments relating to changes in our neighbourhood. I receive regular information about such things," he said to TT.
"This is still worrying and does nothing to contribute to the easing of tensions in our region. It affects all the countries around the Baltic Sea, Hultqvist said.
Observers thought that the vessels, which had been based in the Black Sea, would stay in the Mediterranean. But they continued on to the North Sea and on Tuesday night passed the Great Belt in Denmark. They are believed to be heading to the Russian enclave of Kaliningrad, although Nato told UK newspaper the Daily Express that it would not speculate where the ships are heading.
According to Tomas Ries, a senior lecturer at the Swedish National Defence University, Russia's intentions are clear.
"You can see it as a political signal. Putin is very aware that this attracts attention, it is a demonstration of strength," said to TT.
He told Radio Sweden that the ships in the Baltic are a game-changer.
"It is a game-changer because the missiles that are involved, which have a range of 2600 kilometres against land targets, can be nuclear-tipped and if so, they really cast in doubt the validity of the INF treaty."