Underscoring that threat, Moscow's mayor Sergei Sobyanin said anti-air defences intercepted "most" of the 430 unmanned aerial drones fired by Ukraine towards the capital overnight. The severity of the damage was not immediately clear.
Russian social media accounts are full of videos of people queuing for hours to buy petrol and fighting over what little they're allowed.
On the eve of the Nato gathering, which will be held on Tuesday and Wednesday, Zelensky voiced hope that the meeting in Turkey would not be "empty".
Nato Secretary General Mark Rutte has urged member states to "pull their weight" and ensure Ukraine gets what it needs "to defend its sovereignty".
He underlined that Kyiv was "changing the dynamic on the battlefield", referring to efforts to stall Russian ground troops in the east.
That's also about the recent drone strikes, apparently giving Ukraine an edge.
The phrase of the month here is "window of opportunity".
But as the war in the skies has intensified, Russia's ballistic missiles are causing Kyiv real problems.
Ukraine's air force issues a daily tally of the weapons Moscow launches alongside the number intercepted.
On Monday, almost all drones were blocked successfully but the failure rate for missiles was glaringly obvious.
Ukraine did not stop a single ballistic missile in that attack.
It isn't easy: they fly at several thousand kilometres an hour and there just aren't enough US-made Patriot air defence missiles in Ukraine to counter them.
"It is simply absurd that, in today's world, production has still not been scaled up to the level actually required to protect people from ballistic terror," Zelensky said, venting his frustration in a video address on Monday.
He has been calling on European allies to hand over their own stockpiles of Patriot missiles, arguing that they're no good to anyone in storage when civilians are being killed now in Ukraine.
"Russia is placing its bets on ballistic weapons, and those who want peace must place their bets on protection against ballistic attacks," Zelensky argues, setting out his case for meetings in Ankara.
But Patriot systems are in short supply worldwide and it's not clear how many would ever be enough if Russia were to escalate its ballistic attacks further.
That's why Zelensky also talks about Ukraine producing its own equivalent, with Nato help.
The Russian attacks, though, do suggest that Ukraine's deep strikes are getting under the Kremlin's skin.
After years of Russia targeting civilian infrastructure in Ukraine, including power stations in mid-winter, Moscow now accuses Kyiv of "terrorism" for hitting its oil refineries with drones.
Zelensky calls it an "influence campaign" and he will be keen to share details with Nato allies.
The aim is to pressure Putin into peace talks on terms that Kyiv could stomach – that doesn't include surrendering the entire eastern Donbas region, as Moscow still demands.
