"We began talks," Zelenskyy wrote on X in a brief post announcing the start of the negotiations.

In a video shared by the Ukrainian President on X, Zelenskyy could be seen greeting the US envoys at Kyiv's St Sophia Cathedral.

Witkoff and Kushner had earlier met Russian President Vladimir Putin in Moscow.

Sharing details of the meeting, a White House official told NBC News in a statement: "Today, Special Envoy Witkoff and Jared Kushner met with President Vladimir Putin of Russia to advance President Trump's agenda of peace in the Russia-Ukraine War."

"The two sides discussed substantive plans for next steps, which will be announced in the coming weeks, and look forward to equally productive meetings tomorrow in Ukraine," the official said.

Meanwhile, Kremlin spokesman Dmitry Peskov was quoted by Russia's TASS news agency as saying that the meeting indicated an atmosphere of trust existed between the sides, at least through the channel of communication involving the US envoys.

"The very fact that the meeting is taking place means that an atmosphere of trust does indeed exist, at least through this channel of communication, and that it is strengthening," Peskov said.

"As a rule, however, expanded exchanges of such welcoming remarks emerge when there are messages that the head of state considers necessary to convey," he added.

According to the official handle of the Russian President, Putin also spoke positively about the engagement during his meeting with the US envoys.

"No matter what happens next, contacts of this kind are certainly always beneficial," Putin was quoted as saying.

"The quality of mediation and trust in those who are engaged in it are very important. I'd like to tell you that we find it comfortable to work with you, and, of course, we have a very high level of trust during this work," he said.

According to media reports, the meeting between Putin and the US envoys lasted around three hours.

The talks in Ukraine mark the first time that Witkoff and Kushner have held such negotiations on Ukrainian soil.

Ukrainian delegations have previously travelled to the US for talks over the past several months as part of efforts to find a diplomatic resolution to the conflict.

According to a report by the Kyiv Post, Witkoff and Kushner travelled to Kyiv by train after arriving in Ukraine earlier on Sunday.