With his troops under strain on the front line after more than three years of fighting Russia's bigger invading army, Zelensky was due to begin meetings with leaders gathered in New York this week for the UN General Assembly.
Peace efforts set in motion by US President Donald Trump since he returned to office in January appear to have stalled.
Trump's Alaska summit with Russian President Vladimir Putin and a White House meeting with Zelenskiy and key European leaders took place more than a month ago, but the war has continued unabated.
Zelenskiy said he met late on Monday in New York with Keith Kellogg, Trump's special envoy.
Kellogg and Zelenskiy discussed co-operation agreements on the manufacturing of drones and Ukraine's purchase of American weaponry, the Ukrainian president said on Telegram.
European leaders have supported Zelenskiy's diplomatic efforts, even as the Israel-Hamas war in Gaza is expected to take centre stage at the United Nations.
Some European countries are alarmed by the possibility that the war could spread beyond Ukraine amid what they have called Russian provocations.
NATO allies will hold formal consultations at Estonia's request on Tuesday, after the Baltic country said that three Russian fighter jets entered its airspace last week without authorisation.
Meanwhile, the full-scale war, which began on February 24, 2022, continues to take a heavy toll on Ukrainian civilians.
The UN Office of the High Commissioner for Human Rights said earlier September that Ukrainian civilian casualties increased by 40 per cent in the first eight months of this year compared with 2024, as Russia escalated its long-range missile and localised drone strikes.
Also, a UN Human Rights Office report released Tuesday described the dire situation of thousands of civilians detained by Russia in areas of Ukraine it has captured.
"Russian authorities have subjected Ukrainian civilian detainees in occupied territory to torture and ill-treatment, including sexual violence, in a widespread and systematic manner," the report said.
Russian aircraft dropped five glide bombs on the southern Ukrainian city of Zaporizhzhia during the night, killing a man, regional head Ivan Fedorov said on Tuesday.
In the Odesa region of southern Ukraine, Russian ballistic missiles struck the town centre of Tatarbunary, killing a woman, regional head Oleh Kiper said Tuesday morning.
Overall, Russian forces launched three Iskander ballistic missiles and 115 strike and decoy drones at Ukraine overnight, the Ukrainian air force said.
It said 103 drones were intercepted or jammed, but 12 drones and three missiles reached their targets at six locations.
Moscow Mayor Sergei Sobyanin said that more than 40 Ukrainian drones flying towards the Russian capital were shot down between Monday evening and midday on Tuesday.
Flights were temporarily halted overnight in and out of Moscow's Sheremetyevo airport, causing delays and cancellations, because of the attack.
The Russian defence ministry reported it intercepted 69 Ukrainian drones over a number of Russian regions and the annexed Crimean Peninsula.
