The Ukrainian president mocked Mr Musk’s peace deal at an event organised by The New York Times and asked him to visit the European country instead.
“I think that either someone has influence over him, or he somehow draws conclusions on his own,” Mr Zelensky said by video link at the summit.
He added: “If you want to understand what Russia has done here, come to Ukraine and you will see this with your own eyes.”
“After that, you will tell us how to end this war, who started and when we can end it.”
Last month, the world's richest person sparked controversy by suggesting Russia’s war could be ended by re-running “referendums” in four Moscow-occupied Ukrainian regions organised by the UN and acknowledging Russian sovereignty over the Crimean peninsula.
Mr Musk also launched a Twitter poll asking whether “the will of the people" should decide if seized regions remain part of Ukraine or become part of Russia.
In a sarcastic response, Mr Zelenskyy posted a Twitter poll of his own asking “which Elon Musk do you like more? One who supports Ukraine or one who supports Russia”.
Mr Musk replied: “I still very much support Ukraine, but am convinced that massive escalation of the war will cause great harm to Ukraine and possibly the world.”
At Wednesday’s event, when the video link got disconnected for a brief period, Mr Zelensky quipped that Mr Musk might somehow be behind the incident.
The president said Ukrainians were thankful for the bipartisan US assistance. “Our people are fighting for our shared values, for freedom and democracy, not just in Ukraine but in the whole world,” he said.
“If Ukraine does not stand through this war, the war will spread to other territories.”
He said nearly six million Ukrainians are still enduring the Russian war without any electricity in most regions of the country amid freezing temperatures.
“The situation remains very difficult in the capital, as well as in the Kyiv, Vinnytsia, Lviv, Odesa, Khmelnytskyi and Cherkasy regions,” the president said in his nightly address.
“Energy workers and utility workers, all our services are doing everything to stabilise the system and give people more energy for longer.”