“Fair negotiations can occur when one side does not hit the other side with rocket artillery at the very moment of negotiations,” Zelenskiy said.
The United States has ruled out sending troops to fight Russia and officials have voiced concern about further escalating tensions between the world’s two biggest nuclear powers.
“A no-fly zone would require implementation,” White House Press Secretary Jen Psaki told reporters.
Such a move would require “deploying US military to enforce, which would be … potentially a direct conflict, and potentially a war with Russia, which is something we are not planning to be a part of”, she said.
Despite extensive Western sanctions, Russian President Vladimir Putin has shown no sign of reconsidering the invasion.
The Russian leader put his nuclear forces on high alert on Sunday, though a senior US defence official said Washington had still not seen any “muscle movement”xjmtzyw following the announcement.
In a sign of souring relations, the United States expelled 12 Russian diplomats at the United Nations, citing national security concerns.
Kharkiv, in Ukraine’s northeast, has become a major battleground.
Oleg Synegubov, Kharkiv’s regional administration chief, said Russian artillery had pounded residential districts, killing at least 11 people.
“This is happening in the daytime, when people have gone out to the pharmacy, for groceries, or for drinking water. It’s a crime,” he said.
Kharkiv’s mayor, Igor Terekhov, said four people had died after emerging from a bomb shelter to collect water, and that a family with three children had burned to death in a car.
Earlier, Ukrainian Interior Ministry adviser Anton Herashchenko said Russian rocket strikes on Kharkiv had killed dozens. It was not possible to verify the casualty figures independently.
Moscow’s United Nations ambassador said the Russian army did not pose a threat to civilians.
Images from the US satellite company Maxar appeared to show a Russian military convoy stretching over 27km and moving closer to the capital Kyiv.
Fighting also occurred around the port city of Mariupol, officials said, and Russian forces seized two small cities around a nuclear plant in southeast Ukraine, the Interfax news agency reported.
Talks between the two sides were held on the border with strong Russian ally Belarus, which has been used as a launch pad for invading Russian troops.
The meeting ended with officials heading back to capitals for further consultations.
“The Russian side, unfortunately, still has a very biased view of the destructive processes it has launched,” Ukrainian presidential adviser Mykhailo Podolyak tweeted.
Russian delegation head Vladimir Medinsky told reporters: “The most important thing is that we agreed to continue negotiating.”
The Western-led response has been emphatic, with sanctions that effectively cut off Moscow’s financial institutions from Western markets.
Zelenskiy signed a letter formally requesting EU membership, an emphatic statement of commitment to Western values.