The trip by the US delegation follows a meeting with Russian President Vladimir Putin in Moscow on Saturday as both sides have escalated their aerial attacks in the more than four-and-a-half-year war.
Kremlin aide Yuri Ushakov described Saturday's meeting as "highly useful" while a White House official told Reuters that next steps would be announced in the coming weeks.
The two envoys met Zelenskiy and other top Ukrainian officials in central Kyiv.
After the first round of talks between Ukrainian and US negotiators that lasted about three hours, the US envoys said that they were looking forward to making more progress.
"Substantive, important, and we are very encouraged," Witkoff told reporters after the talks, which also included a working lunch.
Zelenskiy said that more talks, which would also include European representatives, were planned later on Sunday.
UK, French and German security advisers were in Kyiv on Sunday.
"Security guarantees are needed. A dignified post-war peace is needed. Our proposals have been drawn up," Zelenskiy said as his negotiating team was preparing to meet US envoys.
Witkoff and Kushner, Trump's son-in-law, have visited Moscow several times in their roles as peace envoys.
But Sunday is their first visit to Kyiv in their capacity as US negotiators.
Zelenskiy said after the meeting on Sunday that the territorial question "remains relevant" but reiterated his view that such difficult issues "can only be resolved at the level of leaders".
He said that the talks also touched on long-term security guarantees and economic support for Ukraine's postwar reconstruction.
He said that a strong Ukrainian army remained "one of the main guarantees of security".
Zelenskiy said that the sides had agreed to hold a follow-up meeting involving Ukraine, the United States and European countries although a location has not been set.
Witkoff said that the US was pursuing "a diplomatic resolution to this conflict, not a kinetic resolution".
Referring to the previous day's talks, he said that the meeting in Moscow had produced "new ideas" that were later brought to Kyiv.
Both sides would need to make compromises, Witkoff said, adding: "We think we have the ingredients to get to that place."
Although the front lines of the ground war remain largely static, both Russian and Ukrainian forces have intensified long-range air strikes in recent weeks.
Russia has pounded the Ukrainian capital day and night with missiles and drones for the past two weeks, including an attack on Friday on the headquarters of the SBU security service.
The Kremlin has said it would pause strikes on Kyiv until Monday while Zelenskiy has said Ukraine would also halt strikes on Moscow.
with Reuters
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