On Thursday, Russian state media reported Putin as saying: "It all comes down to this. Either we liberate these territories by force of arms or Ukrainian troops will leave these territories and stop fighting there."
State media said Putin's comments were made during an interview with news outlet India Today, which came ahead of the Russian president's two-day visit to the country.
Tuesday's talks in Moscow were also attended by Trump's son-in-law Jared Kushner.
When asked by a reporter on Wednesday if Witkoff and Kushner believed Putin wanted an end to the war, Trump said Putin "would like to end the war. That was their impression."
But Ukrainian Foreign Minister Andrii Sybhia accused Putin of "wasting the world's time", while Ukraine's ambassador to the US said they do not "need to wait for promises from Russia".
There was "not too much progress" at this stage of the talks, ambassador Olga Stefanishyna said, but that they were ongoing.
"It is clear on both sides - in Ukraine and the United States - that Ukraine is committed to the result. Ukraine has invested a lot in the commitment to have a just and lasting peace in our country," she explained.
Earlier on Wednesday, Ukrainian President Volodymyr Zelensky said "the world clearly feels that there is a real opportunity to end the war", but negotiations must be "backed by pressure on Russia".
The US-Russia talks at the Kremlin followed days of US meetings with Ukrainian and European leaders, after concerns had been expressed that the draft of a peace deal was too slanted towards Russia's demands.
"Some of the US proposals look more or less acceptable, though they need to be discussed further", Putin's foreign policy aide Yuri Ushakov said, while adding that others had been openly criticised by Russia's leader.
Although Ushakov did not elaborate further, at least two major points of contention remain between Moscow and Kyiv - the fate of Ukrainian territory seized by Russian forces and security guarantees for Ukraine.