Russia scrapped a plan to bring its troops home on Sunday due to increased tensions in the region.
The foreign state closest to the Ukrainian capital of Kyiv is Belarus, a firm Russian ally.
The West believed that Russia was preparing for an invasion by putting troops in Belarus.
When the end of the exercises came, the plan was changed to carry out joint exercises and withdraw.
According to an official statement, the Russian troops would stay because of increased military activity near the borders.
The area of eastern Ukraine that contains the rebel-held regions of Donetsk and Luhansk is called Donbas. Russia has supported the rebels for a long time, and in February they began giving warnings of bad activity by the Ukrainians, which western officials say is part of the plan to create a pretext for war.
The military drills started ten days ago and were described by Russia's defense ministry as being to practice averting and repelling external aggression.
The Russian troops were on the verge of leaving, according to a few days ago.
Uladzimir Makey, the country's foreign minister, said that not a single soldier, not a single piece of military equipment will remain after the exercises.
Russia preserves its shortest route to strike Kyiv because it didn't withdraw troops.
US officials say that Russia has amassed as many as 190,000 troops around Ukraine, despite denying that it plans to attack.
There are positions along the eastern Ukraine-Russia border, and in the annexed peninsula of Crimea.
President Joe Biden said on Friday that he was certain that Putin would launch an attack in the coming days.
The analysis shows that Russia could target the city of Kyiv from the north.
Satellite images taken this week show a temporary pontoon bridge over the Pripyat River, less than four miles from the Belarus-Ukraine border.
CNN previously reported that the construction could be used to cross the river and advance towards Kyiv.