"Such an array of crimes against the foundations of the national security of the state ... pose very serious questions to the relevant leaders," Zelenskiy said in a Telegram post.
Kyiv and the West say the conflict is an unprovoked attempt to reconquer a country that broke free of Moscow's rule with the break-up of the Soviet Union in 1991.
Moscow calls the invasion a "special military operation" to demilitarise its neighbour and root out nationalists, says it uses high-precision weapons to degrade Ukraine's military infrastructure. Russia has repeatedly denied targeting civilians.
Russian Defence Minister Sergei Shoigu ordered military units to intensify operations to prevent Ukrainian strikes on areas held by Russia, according to a statement from the ministry.
His remarks on Saturday appeared to be a direct response to what Kyiv says is a string of successful strikes carried out on 30 Russian logistics and ammunitions hubs, using several multiple launch rocket systems recently supplied by the West.
The strikes are causing havoc with Russian supply lines and have significantly reduced Russia's offensive capability, according to Ukraine's defense ministry.
Ukrainian officials say the new US-made High Mobility Artillery Rocket Systems (HIMARS) they began receiving last month allow them to reach targets in Crimea, which was annexed by Russia in 2014, and other areas occupied by Russia.
"Good morning from HIMARS," Andriy Yermak, chief of staff to Ukraine's president, wrote on Telegram on Sunday alongside a video showing a large explosion which he said was another destroyed Russian ammunition depot in southern Ukraine.
On Sunday, former Russian president Dmitry Medvedev said the refusal of Ukraine and NATO powers to recognise Moscow's authority over Crimea represents a "systemic threat" for Russia, which has the headquarters of its Black Sea fleet there.
A spokesperson for the Odesa regional administration, Serhiy Bratchuk, said on Telegram late on Sunday that a "significant number" of Russian warships moved from Crimea to Novorossiyisk, along Russia's Black Sea Coast.
Russian-backed separatists have said HIMARS rockets killed two civilians and damaged a bus depot and several other buildings in Alchevsk, east of Solviansk. Ukraine's armed forces said they struck the bus depot because they had the information it was being used to house Russian troops.
The Russian defence ministry said its forces had destroyed a launch ramp and reloading vehicle for one of the HIMARS systems deployed near the eastern city of Pokrovsk.
The head of Pokrovsk regional police, Ruslan Osypenko, said a residential area had been shelled by Russia with multiple rocket launchers and there were dead and wounded. It released a video of damaged homes and residents describing the attack.
