One police officer was killed and 12 people, including four police officers, were injured in an attack on Orikhiv town in Zaporizhzhia region, interior minister Ihor Klymenko said on Telegram.
He said Russian troops used a guided aerial bomb.
An elderly woman was killed in a separate attack in Kharkiv.
"This morning, around 5.10, the enemy fired on Kupiansk-Vuzlovyi village in Kupiansk district," Kharkiv governor Oleh Synehubov said on the Telegram messaging app.
"A residential building was damaged.
"A 73-year-old woman died."Â
Reuters could not independently verify the details of the Ukrainian reports.
Eastern parts of the Kharkiv region and most of the Zaporizhzhia region are directly adjacent to the frontline, and Ukrainian forces have reported an increase in Russian attacks there in recent weeks.
Kharkiv regional authorities earlier this month announced the mandatory evacuation of civilians from settlements closest to the front line in Kupiansk district.
Ukrainian authorities said this week Russia attacked a "civilian infrastructure object" in Zaporizhzhia on Thursday evening.
Russia denies deliberately targeting civilians during its invasion of Ukraine, which is now in its 18th month and has resulted in the deaths of thousands of people, the uprooting of millions and the destruction of Ukrainian towns and cities.
On Friday, Ukrainian officials said Russia attacked the western Ukrainian region of Ivano-Frankivsk with hypersonic missiles, hitting areas near a military airfield and killing an eight-year-old boy.
One missile crashed into the grounds of a family's home in the Kolomyia district, wounding several people including the boy, who later died in hospital, regional governor Svitlana Onyshchuk said.
"Medics did everything possible, but unfortunately the child's life could not be saved," she wrote on the Telegram messaging app without clarifying how many people had been hurt.
Air defences shot down one of the four Kinzhal missiles near the capital Kyiv as they hurtled towards western Ukraine hundreds of kilometres from the front, the air force said.
"One X-47 (hypersonic) missile was destroyed within Kyiv region," it said on Telegram.
"The rest hit near the airfield.
"Civilian infrastructure was damaged, and one of the missiles hit a residential area."
Air Force Colonel Yuriy Ihnat suggested the attack had been aimed at Ukrainian pilots who were about to travel to the West to train to use F-16 fighter jets that Kyiv hopes will eventually be delivered.
