Kyiv says the strikes are fair retribution for Russia's more than four-year barrages on Ukraine and that it is a bid to force Russia to the negotiating table.
Ukrainian drone strikes hit southern Russian oil refineries and the port of Taganrog on the Azov Sea on Friday, where authorities declared an emergency and evacuated some residents, officials said.
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Kyiv has beefed up its efforts in recent months to hinder Moscow's financial capabilities in its war against Ukraine, targeting energy infrastructure in retaliatory strikes and causing a nationwide fuel shortage.
Russia's defence ministry said its forces downed over 370 Ukrainian drones, including over the Moscow region.
In the port of Taganrog, near occupied Ukraine, social media videos showed plumes of smoke rising over the city.
Local governor Yuri Slyusar said he visited the port after "massive" night-time strikes.
"Efforts to extinguish the fire of petroleum products at the seaport are ongoing."
Slyusar said several dozen of the city's residents had been moved to temporary accommodation.
"I told them frankly: unfortunately, it will not be possible to extinguish this type of fire quickly," he said.
Earlier Slyusar said drones had hit two "oil storage facilities" in the town of Azov.
In the neighbouring Krasnodar region, authorities said drones caused a fire at the Ilsky oil refinery.
Authorities reported no casualties.
Russian leader Vladimir Putin has acknowledged that the Ukrainian strikes are causing a fuel shortage and said they are aimed at dividing Russians.
US President Donald Trump, asked about Kyiv's strikes during a meeting with Ukraine's Volodymyr Zelensky this week, appeared to endorse the campaign.
"It's an escalation, but it's also an escalation that can help lead to an end," Trump said.
The Kremlin said Ukrainian military pressure would not force it into concessions.
"We see certain misconceptions within the White House administration, that by escalating military pressure it can help move to a peace settlement. That is a mistaken view," Kremlin spokesman Dmitry Peskov told reporters.
Kyiv says the strikes are fair retribution for Russia's more than four-year barrages on Ukraine and that it is a bid to force Russia to the negotiating table.
Ukraine's army chief says war not yet at 'turning point'
Meanwhile, Ukraine's commander-in-chief Oleksandr Syrsky said on Friday that a turning point in the war with Russia was "still a long way off," despite hailing a string of recent successes for his troops.
Kyiv's army has halted the Russian advance across much of the front line in recent months and delivered a string of major long-range attacks on Russian oil refineries.
Many in Ukraine and among their backers abroad are saying Kyiv's troops are on the front foot in the more than four-year war.
In a social media post summarising the first half of the year, Syrsky noted a decrease in the number of "active offensive fronts" and said Russia's assaults had dropped by half.
"In terms of the rate of advance, the two sides have effectively reached parity," Syrsky said.
"At the same time, the enemy must not be underestimated. We are still far from a turning point in the war," he added.
Syrsky also said Ukraine had carried out successful strikes on 697 targets inside Russia over the last six months as it upped its own campaign of retaliatory long-range attacks.