President Zelensky has urged countries to hit Russia with more sanctions in response to "a new wave of terror" after Monday's attacks on Ukraine.
At least 19 people were killed and scores more injured as Russian missiles hit regions across the country.
Defiant, he said the attacks will only "delay our recovery a little".
Following more strikes on Tuesday, Mr Zelensky called on the West to find new ways to apply political pressure to Russia and support Ukraine.
The calls came after he met the G7 group of nations for emergency virtual talks on Tuesday.
The bloc - which consists of Canada, France, Germany, Italy, Japan, the UK and US - promised to continue providing "financial, humanitarian, military, diplomatic and legal" support to his country "for as long as it takes".
Mr Zelensky said: "For such a new wave of terror there must be a new wave of responsibility for Russia - new sanctions, new forms of political pressure and new forms of support for Ukraine."
"The terrorist state must be deprived of even the thought that any wave of terror can bring it anything."
Russian President Vladimir Putin said the attacks were retaliation for Saturday's explosion on a key bridge linking Russia to Crimea.
Western countries have already placed widespread sanctions against Russian businesses as well as allies of President Putin since the invasion of Ukraine in February.
This includes removing major Russian banks from the international financial messaging system Swift, and sanctioning more than 1,000 Russian individuals and businesses - including oligarchs.
While the US has banned all Russian oil and gas imports, the EU has been reluctant to do so because it relies on Russia for about 40% of its gas needs.
Monday's barrage of missile strikes was the heaviest bombardment Ukraine has seen since the early days of the war. Several strikes hit Kyiv - the first time the capital city has been targeted in months, and previous attacks have not hit the city centre.
Civilian areas including a popular park and children's playground were hit during the morning rush hour. Infrastructure was destroyed, causing a power blackout in many neighbourhoods.
On Tuesday, President Zelensky said 28 more missiles were fired, 20 of which were shot down. These included Iranian combat drones, he said. The BBC has not been able to verify this.
"If it wasn't for today's strikes, we would have already restored the energy supply, water supply and communications that the terrorists damaged yesterday," the president said in his nightly address on Tuesday evening.
"Today, Russia will achieve only one additional thing: it will delay our recovery a little."
He added that restoration works were taking place "quickly and efficiently" throughout the country, and that electricity and communication had been restored to most cities and villages targeted in Monday's attacks.
"Where there was destruction, the infrastructure will be renewed everywhere. Where there were losses, there is already or will be construction," he said.
On Tuesday, reports also emerged of a mass grave being found in recently liberated Lyman, in the eastern Donetsk region.
Pavlo Kyrylenko, head of the Donetsk region's military administration, was quoted by Associated Press as saying that more than 50 bodies of soldiers and civilians had been found in a series of graves. They included Ukrainian soldiers buried together in a mass grave, as well as individual graves holding the bodies of civilians.
"We are finding bodies and parts of bodies here," Mr Kyrylenko said.
Lyman was liberated by Ukrainian troops last month, as part of a rapid counteroffensive that recaptured large parts of the east of the country from Russian forces.
Meanwhile in Washington, US President Joe Biden told CNN he believed Vladimir Putin was a "rational actor" who misjudged his ability to successfully invade Ukraine.
"I think he thought he'd be welcomed with open arms - that this was the home of mother Russia in Kyiv and he was going to be welcomed - and I think he totally miscalculated," Mr Biden said.
Asked about the prospects of meeting President Putin at next month's Group of 20 summit in Indonesia, Mr Biden said he did not currently see a reason to do so.
"It would depend on specifically what he wanted to talk about," the US president said, adding that he would be open to discussing Brittney Griner, the American basketball star currently serving a nine year prison sentence in Russia on drug charges.
"But look, he's acted brutally. I think he's committed war crimes, so I don't see any rationale to meet with him now," Mr Biden told CNN's Jake Tapper.
President Biden also said he didn't believe Mr Putin would resort to nuclear warfare, despite apparent threats to do so.
"I think it's irresponsible for him to talk about it, the idea that a world leader of one of the largest nuclear powers in the world says he may use a tactical nuclear weapon in Ukraine," Joe Biden said.
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