The advance towards the city of Sumy - the administrative centre of the Sumy region - comes as Kyiv showed its ability to continue fighting by conducting a series of strikes in recent days, hitting Russian strategic bombers and the Crimean Bridge.
Russian and Ukrainian delegations met in Turkey for peace talks on Monday where Moscow said it would only agree to end the war if Kyiv cedes big new chunks of territory and accepts limits on the size of its army.
On Tuesday, Russia's defence ministry said its forces took control of Andriivka, after capturing several other villages in recent days. Kyiv said Russian artillery attack on the city of Sumy killed four people and injured 28.
Ukraine President Volodymyr Zelenskiy on X called the Russians "sleazebags" for targeting "ordinary residential buildings".
The head of the military administration of the Sumy region, which lies north of Ukraine's second-largest city of Kharkiv, held a meeting on Tuesday to discuss the region's defence strategy.
"The situation in the border area of Sumy region remains complex, dynamic, but controllable," the head of the military administration, Oleh Hryhorov, said on Facebook.
"The Russian army is constantly shelling border villages, hitting residential buildings, farms, and civilian infrastructure facilities."
The dual advance with fierce frontline fighting and missile and drone strikes in Sumy hinders Ukraine's defence abilities along in the southeast Donbas region, of which Moscow is seeking full control, military analysts say.
On Monday, Ivan Shevtsov, a spokesman for the Ukrainian brigades fighting in Sumy, told Ukrainian national broadcaster that Russian forces had captured about 15km along the frontline, going six-to-seven kilometres deep.
If Russian advances take the town of Yunakivka, Shevtsov said, the city of Sumy will be under a direct threat.
The Ukrainian Deep State blog of analysts who track the front line using open sources said Russian forces are moving to within 20-25 km of Sumy, putting the city within a range of shorter-range attack drones.
Reuters could not independently verify the Russian claim of capturing Andriivka and Ukraine's General Staff made no references to the village in its evening battlefield report. DeepState said early on Wednesday that Andriivka was now in Russian hands.
Over the weekend, Sumy's authorities ordered mandatory evacuation of 11 additional villages due to escalating Russian attacks.
Shevtsov said Russia wants to completely capture the Sumy region, not just make a small incursion.
"Just ... like other regions in eastern Ukraine," he added.
