Russia’s defence ministry says its forces have destroyed dozens of drones in several regions across the country, including Moscow.
The biggest attack happened in the southern Russian region of Krasnodar, where an oil refinery was targeted.
The attacks come as Russia holds a general election in which President Vladimir Putin is guaranteed to win.
In Ukraine, officials reported an overnight barrage of Russian drones and missiles on the port city of Odesa.
The Ukrainian governor of the north-eastern city of Kharkiv said 15 settlements had been shelled by Russia over the past 24 hours.
In Russia, authorities said 17 drones had been launched against an oil refinery and had been neutralised, but one sparked a fire as it fell.
No deaths were reported as a result of the fire, which has been extinguished.
One person is thought to have died of a heart attack during the strike. It is the sixth oil refinery attacked in Russia over the past week.
A source has confirmed to the BBC that Ukrainian forces targeted the Slovyansk oil refinery in the Krasnodar region of southern Russia. The security source referred to a “successful result”, and a “large fire”.
It said again that Ukraine’s aim was to undermine the Russian economy and its oil exports.
The Krasnodar attack is the latest in a number of similar drone attacks, with 12 oil refineries targeted in recent times.
Meanwhile, Moscow Mayor Sergei Sobyanin wrote on Telegram that five drones were downed in different areas while flying towards the capital early on Sunday.
And two Moscow airports have imposed flight restrictions for security reasons, state media report.
Another area of Russia – the Belgorod region, near northern Ukraine – has also come under attack, according to its governor. In the early hours of Sunday, he said a teenage girl had died when a shell hit a residential building.
Vyacheslav Gladkov said drones dropped explosive devices in the village of Oktyabrsky – damaging electricity and gas supply lines.
Later on Sunday, Mr Gladkov said a man died “before an ambulance crew arrived” after air strikes hit a car park in Belgorod. Eleven others were injured, the governor added.
It is the second time Belgorod has been targeted this weekend.
On Saturday, at least two people were killed in a bombardment the authorities blamed on Ukraine. Shops and schools were closed afterwards as a safety precaution.
According to Ukraine’s southern defence forces, 13 Iranian-made Shahed drones were shot down.
No injuries were reported, but the attack caused fires at two agricultural sites and destroyed buildings. The fires have since been put out.
Another drone was shot down in the Mykolaiv region.
While Russia claims that Ukraine is attempting to disrupt the presidential election that is certain to give President Putin another six years in power, it also launched a wave of drones against Ukrainian cities overnight – as it has done since the start of the full-scale invasion in February 2022.
Ukrainian forces managed to intercept most of them, but two struck sites in the port city of Odesa – days after a double missile attack killed at least 20 people and left dozens more wounded.
In his evening address on Saturday, President Volodymyr Zelensky referred to the success of Ukraine’s long-range drones in recent weeks exposing what he called “vulnerabilities” in Russia’s “war system”.
“Ukraine will now always have its own strike force in the sky,” he said.