Visiting a high school in Kontiolahti, near Joensuu, on Monday, the premier suggested that this could begin on a trial basis as part of a planned reform of the national curriculum.
Decisions on the curriculum reform are being finalised this autumn. Kiviniemi noted that it might already be too late to add changes that would take effect in the autumn of 2011.
Several schools in North Karelia, where Kontiolahti is located, have asked for permission to replace obligatory Swedish with Russian. For instance, the border municipality of Tohmajärvi applied for such permission, but was blocked by the Ministry of Education.
Kiviniemi did not say whether she thought that Swedish could be completely replaced by Russian, or whether she meant that pupils would still need to study Swedish in any case.
As the country's second official language, Swedish remains obligatory at all schools. However in Eastern Finland Russian speakers far outnumber Swedish speakers. Most of the nation's 5.4 percent Swedish-speaking minority is concentrated along the coast.
Finland was ruled by Sweden for centuries, and was then an autonomous Grand Duchy of Russia between 1809 and 1917.