The incursion began on Friday as Russian troops breached Ukraine's border near Kharkiv city, establishing a northeastern front in a conflict that has primarily unfolded in the east and south over the past two years.
Putin said Finland and Sweden's entry into NATO is 'a meaningless step', adding that Russia will deploy troops and systems of destruction on the Finnish border following its accession to the alliance last April.
The inquiry, overseen by the Ukraine prosecutor general's office, comes in the wake of a video shared by the Ukrainian government on social media, depicting the incident near an observation post outside the village of Stepove near Donetsk in eastern Ukraine.
Vyacheslav Gladkov, governor of Russia's Belgorod region, said there was more shelling of a border area later Wednesday, which he blamed on Ukrainian forces.
Ukraine has claimed that 400 Russian soldiers were killed and 300 others were injured after Ukrainian forces hit a military base of Moscow in Makiivka.
Rain and soft soil in late November will slow down the movement of both Ukrainian and Russian troops. Possible heavy snowfall and cold weather could also slow down operations on the battlefield.
After Russian troops retreated from Ukraine's southern city of Kherson on Friday, Moscow established that the Ukrainian city of Genichesk is now Kherson region's temporary administrative capital. Genichesk is a port city on the Sea of Azov known for its resorts, according to TASS.
Amid the ensuing battle between Russia and Ukraine, the US on Thursday announced $400 million worth of security assistance for Ukraine, a day after Russia ordered withdrawal of its troops from Kherson.