Witkoff spent almost five hours with Putin in Moscow on Tuesday, after which the Kremlin said "no compromise" had been reached on a draft US peace plan.
The Kremlin said Putin was ready to continue meeting the Americans "as many times as needed", but Ukraine and its allies in Europe have called into question the Russian leader's commitment to ending the war.
On Friday, Ukrainian President Volodymyr Zelensky said he wanted to "obtain full information about what was said in Moscow and what other pretexts Putin has come up with to drag out the war".
Kyiv pushed for revisions to the initial US peace plan, which was widely seen as favourable to Moscow when an initial version leaked to the media. An updated version has not been shared publicly.
Major points of contention remain between the two sides, including security guarantees for Ukraine post-war and territorial concessions.
Russia currently controls roughly one-fifth of Ukraine's territory, including swathes of the Donbas area in the east – made up of the Donetsk and Luhansk regions.
In an interview with India Today on Friday, Putin warned Ukrainian troops to withdraw fully from the region this week, saying Russia would otherwise "liberate these [Donbas] territories by force".
Kyiv and its European allies believe the most effective way to deter Russia from attacking again in the future would be to grant Ukraine membership of Nato, or to provide comprehensive security guarantees.
Russia is staunchly opposed, while Trump too has repeatedly signalled he has no intention of letting Ukraine join the military alliance.
The prospect of Ukraine joining Nato was a "key question" that was tackled in Moscow, the Kremlin said on Wednesday.
Trump said those talks were "reasonably good", but it was too soon to say what would happen as "it does take two to tango".