Speaking in New Jersey late on Sunday, Trump said of Putin: "I've known him a long time, always gotten along with him, but he's sending rockets into cities and killing people, and I don't like it at all."
He also said he was considering increasing US sanctions on Russia – something he has repeatedly threatened to do before.
Trump posted his "crazy" remark shortly afterwards, adding on Truth Social: "I've always said that he wants all of Ukraine, not just a piece of it, and maybe that's proving to be right, but if he does, it will lead to the downfall of Russia!"
But the US president also had strong words for Zelensky, saying that he was "doing his country no favours by talking the way he does".
"Everything out of his mouth causes problems, I don't like it, and it better stop," Trump wrote of Zelensky.
Despite Kyiv's European allies preparing further sanctions for Russia, the US has said it will either continue trying to broker these peace talks, or "walk away" if progress does not follow.
Peskov said on Monday that Russia was "truly grateful" to the Americans and "personally to President Trump" for their help in organising and launching this negotiation process.
Last week, Trump and Putin had a two-hour phone call to discuss a US-proposed ceasefire deal to halt the fighting.
The US president said he believed the call had gone "very well", adding that Russia and Ukraine would "immediately start" negotiations toward a ceasefire and "an end to the war".
Ukraine has publicly agreed to a 30-day ceasefire but Putin has only said Russia will work with Ukraine to craft a "memorandum" on a "possible future peace" – a move described by Kyiv and its European allies as delaying tactics.
The first direct Ukrainian-Russian talks since 2022 were held on 16 May in Istanbul, Turkey.
Aside from a major prisoner of war swap last week, there was little or no progress on bringing a pause in fighting closer.
Russia currently controls about 20% of Ukrainian territory. This includes Crimea – Ukraine's southern peninsula annexed by Moscow in 2014.