Zelensky said on Saturday morning that the target areas for the attack in and around St Petersburg were about 850km (528 miles) from the Ukrainian border.
The extent of the damage was not immediately clear, but a video posted by Ukraine’s president showed a small plane flying toward the target and thick black smoke billowing from the area after the strike.
The BBC later confirmed that the St Petersburg oil terminal had been hit.
The Ukrainian military described the terminal as “one of the largest” in Russia, capable of producing 12.5 million tons of fuel products per year.
The military also said Russia’s Baltic Fleet naval base in Kronstadt had been hit.
Russia has not publicly commented on the claim.
Governor Beglov said 72 Ukrainian drones were shot down over St Petersburg and the wider Leningrad region.
He urged the city’s residents to stay indoors until the drone threat is over. Mobile internet services could also be disrupted, he warned.
More than five million people live in St Petersburg.
In another development on Saturday, the Ukrainian military denied that the key eastern Ukrainian city of Kostyantynivka is now under full Russian control.
Military spokesman Maj Andriy Kovalyov told the BBC that “Kostyantynivka is still under the control of the Defense Forces of Ukraine”.
He admitted that there were “incidents of infiltration by small infantry groups deep into the combat systems of our forces”, but added that those groups were known and destroyed.
His comments came a day after Putin said Russian control had been established in the town of Kostyantynivka in June.
The Kremlin leader did not provide evidence to support his claim.
Later on Saturday, Zelensky wrote in Telegram: “If Kostyantynivka is now under Russian control, then Putin will probably have no problem meeting with me there and find diplomatic solutions to finally end the war. But still, he will not fall forward: the reality is very different from Putin’s words.”
Kostyantynivka is one of the heavily fortified towns that make up Ukraine’s “fortified belt” in the Donetsk region, most of which resides in Russia.
In its latest operational report on Saturday afternoon, the Russian Defense Ministry said it had shot down more than 500 Ukrainian drones and missiles launched throughout the night and early morning.
It described the attack on Ukraine as an attempt by Zelensky to “distract the attention” of the Ukrainian people and “foreign sponsors” from the consequences of the massive and deadly Russian strike on the Ukrainian capital Kyiv on July 2 and the “catastrophic failure” of the Ukrainian forces in Kostyantynivka.
Ukraine’s attacks on Russian civilian centers “will not go unanswered”, the ministry said.
Both sides – it seems – want to gain the upper hand before next week’s NATO summit in Turkey.
On Saturday, Putin sent President Donald Trump a congratulatory note to mark the 4th of July celebrations in the US, calling for “constructive relations” between their countries.
On Friday, the Russian leader visited the commanders dressed in military fatigues, where he made his claim about the capture of Kostyantynivka.
Zelensky said Putin chose to lie to the world about the ongoing situation.
This is still a war of words and arrows.
Additional reporting by BBC correspondent James Landale in Moscow
