Large contingents of Russian forces are on the offensive in northeast Ukraine's Kupiansk sector and engaged in heavy fighting, Ukrainian officials say.
Overnight air attacks were also launched on Ukraine's south and east using drones and possibly ballistic missiles, according to Ukraine's Air Force.
Ukraine's military launched a counteroffensive in the east and south several weeks ago. But officials have pointed to an intensification of Russian activity near Kupiansk and nearby Lyman, towns in the northeast retaken by Ukraine late last year.
They said large groups of Russian personnel were now trying to break through Ukrainian defence lines in the area.
"For two days running, the enemy has been actively on the offensive in the Kupiansk sector in Kharkiv region," Deputy Defence Minister Hanna Maliar wrote on Telegram on Monday.
"We are defending. Heavy fighting is going on and the positions of both sides change dynamically several times a day."
Serhiy Cherevatyi, spokesman for Ukraine's eastern grouping of troops, said the Russian military had amassed more than 100,000 troops and more than 900 tanks in the area.
This figure, he told national television, compared to Soviet troop levels of about 120,000 at the height of Moscow's 1979-89 war in Afghanistan. Kyrylo Budanov, Ukraine's intelligence chief, estimated in May that 370,000 Russian troops were inside the country.
Russian forces in the area, Cherevatyi said, had drafted in airborne units and their best motorised infantry units.
"The enemy is concentrating everything in order to break through the defences of Ukrainian troops," he said.
"Our soldiers are holding their defences, preventing the enemy from fully seizing the initiative and they are continuously launching counterattacks," Cherevatyi said.
The Russian defence ministry's accounts of fighting in the region said Russian forces had hit Ukrainian positions in several towns in Kharkiv and the neighbouring Luhansk region.
Russian forces, the ministry said, had also repelled 13 Ukrainian attacks further south in Donetsk, including areas near the shattered city of Bakhmut, captured by Russian forces in May after months of battles.
In the south, where Ukrainian forces have focused on capturing clusters of Russian-held villages, Deputy Defence Minister Maliar said Ukrainian forces were proceeding with their drive to reach ports on the Sea of Azov.
Meanwhile Ukraine's Air Force said the southern port of Odesa and the Mykolaiv, Donetsk, Kherson, Zaporizhzhia and Dnipropetrovsk regions were under threat of Russian drone attacks.
Using the Telegram messaging app, the Air Force added that Russia may be using ballistic weaponry to attack the regions of Poltava, Cherkasy, Dnipropetrovsk, Kharkiv and Kirovohrad.
Oleh Kiper, the head of the Odesa region's military administration said air defence systems there were engaged in repelling a Russian drone attacks.
"Several waves of attacks are likely," Kiper said on Telegram.
Reuters could not immediately verify the battlefield claims.
