Ukraine says Russian troops have been spotted at 10 locations in Ukrainian territory, including two major cities controlled by pro-Russian rebels seeking autonomy from Ukrainian rule.
Military spokesman Andriy Lysenko said Russia is continuing to concentrate soldiers and military hardware in six areas in the Donetsk region, including Donetsk city and Luhansk.
Lysenko - speaking Tuesday - also said 15 Ukrainian soldiers have been killed in fighting in the east since early Monday.
Separately, Ukraine's Defense Minister Valeriy Heletey (writing on his Facebook page) said Ukraine military objectives are shifting from a counter-insurgency operation to a battle against the Russian army. He called the fight "our great patriotic war."
NATO estimates at least 1,000 Russian troops are in Ukraine. Moscow has repeatedly denied any military presence in Ukrainian territory.
Meanwhile, the United Nations says the number of people displaced by the Ukraine rebellion has more than doubled in just a month.
The U.N. refugee agency said Tuesday that 260,000 people are displaced inside eastern Ukraine, compared to 117,000 announced in the first week of August.
The director of the UNHCR's Europe Bureau, Vincent Cochtel, told reporters in Geneva that shelling in the region also has left people with limited access to food, water and other basic necessities.
Separately, United Nations Secretary-General Ban Ki-moon called for political dialogue between Russia and Ukraine, saying "there is no military solution" to the Ukraine crisis.
Ban made his remarks during a stop in New Zealand, a day after one of the leaders of the pro-Russian separatists, Andrei Purgin, said they are ready to discuss a cease-fire and prisoner exchange.