Russia breached the truce, to which Kyiv hasn't signed up, 734 times since it started, Ukraine's foreign minister Andrii Sybiha said, adding Moscow had carried out 63 "assault operations".
Kyiv claimed the violations took place in the northern region of Sumy and the east.
One person died and two were wounded when Russian forces dropped guided air bombs on residential areas near the border in the northeast Sumy region, the regional prosecutor's office said.
But just minutes after Mr Sybiha's accusations, Moscow responded with its own claims against Kyiv.
Quoting Russia's defence ministry, state media reported Ukraine broke the ceasefire 488 times.
Russia's defence ministry also claimed on Thursday that Ukraine had tried twice to push through the border in the Kursk region where Ukraine launched a surprise incursion last summer, Russian news agency Interfax reported.
Ukraine has, in recent months, lost ground in Kursk. Russia has claimed Ukrainian troops have been pushed out completely.
