And White House National Security Advisor Jake Sullivan pledged the US would "work with the international community to make sure there's accountability" for what he called "mass atrocities".
Pope Francis called for an Easter ceasefire in Ukraine to pave the way for peace through "real negotiation".
"Let the Easter truce begin. But not to provide more weapons and pick up the combat again -- no! -- a truce that will lead to peace, through real negotiation," he told a public mass at Saint Peter's Square.
The pontiff denounced a war where "defenceless civilians" suffered "heinous massacres and atrocious cruelty".
But Russia's Orthodox Patriarch Kirill, a key Putin ally, issued his own appeal against Russia's "enemies".
"In this difficult period for our fatherland, may the Lord help each of us to unite, including around power," he said.
"This is how true solidarity will emerge in our people, as well as an ability to push back external and internal enemies, and to build a life with more good, truth and love."
'Ready to fight'
The remarks came after Zelensky said Ukraine was readying for a new Russian onslaught.
"We see the preparations for important battles, some people say decisive ones, in the east," he said Saturday at a press conference with visiting Austrian Chancellor Karl Nehammer.
"We are ready to fight and to look in parallel to end this war through diplomacy."
Launching his own diplomatic initiative, Nehammer said he would meet Putin on Monday in a move his spokesman insisted was coordinated with "Berlin, Brussels and... Zelensky".
He will be the first European leader to visit the Kremlin since the invasion began on February 24.
The UN on Sunday said 4,232 civilian casualties had been recorded in Ukraine to date, with 1,793 killed and 2,439 injured.
Ukraine's prosecutor Venediktova said 1,222 bodies have been found in the region around Kyiv alone so far.
At least two corpses were found inside a manhole at a petrol station on a motorway outside Kyiv on Sunday, an AFP reporter saw.
The bodies appeared to be wearing a mix of civilian and military clothing.
A distraught woman appeared at the manhole and peered inside, before breaking down and clawing the earth.
She wailed "my son, my son".
Ukraine said Kremlin propaganda had laid the groundwork for the bloody campaign, accusing Russian media of long sowing aggression towards Ukrainians.
"For many years, Russian political elites and propaganda have been inciting hatred, dehumanising Ukrainians, nurturing Russian superiority and laying ground for these atrocities," Foreign Minister Dmytro Kuleba said on Twitter Sunday.
'Rockets keep flying'
The comments came on the heels of a surprise visit to Kyiv on Saturday by British Prime Minister Boris Johnson.
Hailing the country's response to the Russian invasion, Johnson offered Ukraine armoured vehicles and anti-ship missiles, crucial to halting the Russian naval siege of Black Sea ports, to help ensure that the country will "never be invaded again".
In a bid to shore up international resolve against Moscow, US President Joe Biden was to hold virtual talks Monday with Indian Prime Minister Narendra Modi, just weeks after saying India has been "shaky" in its response to the invasion.
At the same time, EU foreign ministers are to meet to discuss a sixth round of sanctions, even as divisions over a ban on Russia gas and oil imports threatened to blunt their impact.
In further Russian strikes, the airport in Dnipro between central and eastern Ukraine, was hit hard.
"The airport itself and the infrastructure around it has been destroyed. Rockets keep flying and flying," the head of the city's military administration, Valentin Reznichenko, said on Telegram.
An AFP reporter saw black smoke in the sky above the facility but a plane also took off later on Sunday, suggesting its runway was still functioning.
As Russian forces regroup in the east and south of Ukraine, local officials are urging residents to flee before it is too late.
At least two people were killed in bombardment of the northeastern city of Kharkiv and its surroundings, governor Oleg Sinegubov said on Facebook on Sunday, reporting 66 strikes in 24 hours.
"The Russian army continues to wage war on civilians due to a lack of victories at the front," he said.
The mayor of eastern Lysychansk, Oleksandr Zaika, asked residents to evacuate as soon as possible due to constant shelling by the Russian army.
Speaking Saturday from Warsaw, European Commission President Ursula von der Leyen said a global pledging event for the more than 4.5 million refugees who have fled the country had raised 10.1 billion euros ($11 billion).
In another sign of Western solidarity, NATO Secretary General Jens Stoltenberg said the military alliance was drawing up plans for a permanent military force on its border to prevent further Russian aggression.
"What we see now is a new reality, a new normal for European security," he told Britain's Daily Telegraph.