Moscow has escalated its bombardments of Ukraine and Kyiv has retaliated with strikes deep inside Russian territory.
Talks in Turkey last week failed to yield a breakthrough towards ending the three-year war.
Aside from an agreement to exchange prisoners, progress has stalled and Russia has repeatedly rejected calls for an unconditional ceasefire.
After the overnight barrage of more than 300 drones and seven missiles, Ukrainian President Volodymyr Zelensky urged Kyiv's Western allies to respond with "concrete action".
"Action from America, which has the power to force Russia into peace. Action from Europe, which has no alternative but to be strong," Zelensky wrote in a post on social media.
He added that two of the missiles fired in the latest wave attacks were made in North Korea.
Russia's defence ministry said it had targeted "Ukrainian aviation, missile, armoured vehicle and ship-building facilities in Kyiv" with a "group strike".
"The goal of the strikes was achieved. All designated objects were hit," the ministry said.
But residential and hospital buildings were struck in Odesa, where two people were killed and at least nine others were wounded, Governor Oleg Kiper said.
"The enemy massively attacked Odesa with strike drones," Kiper wrote on Telegram.
"The Russians hit a maternity hospital, an emergency medical ward and residential buildings," he said, adding that the maternity hospital had been evacuated in time.
- Prisoner swap -
In central Kyiv, an AFP journalist heard at least a dozen explosions, anti-aircraft fire and the buzzing of drones.
City officials said one woman was killed and four people were wounded.
The mayor said strikes hit at least seven districts, setting buildings and cars on fire.
Russia's 2022 invasion of its neighbour triggered the biggest European conflict since World War II, forcing millions to flee their homes and decimating much of eastern and southern Ukraine.
Ukrainian cities are targeted by Russian air strikes almost daily.
Russia launched a record 479 explosive drones at Ukraine overnight into Monday morning, the Ukrainian Air Force said.
Kyiv has responded with attacks on Russian territory, targeting transport and weapons production infrastructure.
Russia's transport agency Rosaviatsia said on Tuesday that flight operations had been temporarily restricted at more than a dozen Russian airports -- standard procedure during Ukrainian drone attacks.
In the city of Belgorod near the border with Ukraine, Russian emergency services said one person was killed in a Ukrainian drone attack on a petrol station.
Russia's defence ministry said it had intercepted 102 Ukrainian drones overnight.
Despite pressure from US President Donald Trump to reach a ceasefire agreement, peace talks are at a standstill.
The only concrete agreement reached at talks in Istanbul last week was a large-scale prisoner exchange and the repatriation of dead soldiers' bodies.
- Demands -
Russia and Ukraine swapped a first group of captured soldiers on Monday and Zelensky announced the exchange would "continue in several stages over the coming days".
The deal should see the freeing of all captured soldiers under the age of 25, as well as those who are sick or severely wounded.
But Zelensky said last week it was "pointless" to hold further talks with the current Russian delegation -- who he previously dismissed as "empty heads" -- since they could not agree to a ceasefire.
Russian forces meanwhile are making steady advances across the front line.
Over the weekend Moscow said it had pushed its offensive into the Dnipropetrovsk region for the first time, marking a significant territorial escalation.
"Time for everyone to finally accept the fact that Russia understands only strikes, not rational words," Zelensky's top aide, Andriy Yermak, said on Tuesday, in a thinly veiled criticism of the Trump administration.
As a condition for halting its invasion, Russia has demanded that Ukraine cede the territories Moscow says it has annexed and forswear joining NATO.
It has also rejected a proposed 30-day unconditional ceasefire sought by Kyiv and the European Union, arguing that this would allow Ukrainian forces to rearm with Western deliveries.
Ukraine is demanding a complete Russian withdrawal of from its territory and security guarantees from the West.
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