On Sunday Trump suggested, without evidence, that Zelensky was the main obstacle to peace.
He told reporters that Russia was "fine" with the peace plan outlined to both sides by the US, that contained major concessions for Ukraine and which allies feared would leave it vulnerable to a future invasion.
In the Politico interview, he claimed Ukrainian negotiators "loved" the US-backed proposal and alleged Zelensky had not yet read it.
Trump also repeated previous calls for Kyiv to hold elections and claimed it was "using war" as a reason not to do so.
He said: "You know, they talk about a democracy, but it gets to a point where it's not a democracy anymore."
Zelensky's five-year term as president was due to end in May 2024, but elections have been suspended in Ukraine since martial law was declared after Russia's invasion.
Speaking to reporters after Trump's comments, Zelensky said he was "ready for the elections" and he would ask for proposals to be drawn up which could change the law.
Elections could be held in the next 60 to 90 days if security is guaranteed with the help of the US and other allies, he told reporters.
Also in the Politico interview, Trump claimed ideological divisions now threatened to fracture Washington's alliances with Europe.
Asked whether leaders who he viewed as weak could still be allies, he replied: "It depends", adding: "I think they're weak, but I also think that they want to be so politically correct. I think they don't know what to do."
The president's remarks came after his administration released its new 33-page National Security Strategy, which warned of Europe's potential "civilisational erasure" and questioned whether some nations could remain reliable allies.
Russia welcomed that strategy - which did not cast Russia as a threat to the US - as "largely consistent" with Moscow's vision.
Trump also warned on Tuesday many countries in Europe "will not be viable countries any longer" if they keep on the way they are going, adding: "What they're doing with immigration is a disaster."
He singled out Hungary and Poland as doing a "very good job" on immigration, but said most European nations were "decaying".
Responding on Tuesday to the strategy, German chancellor Friedrich Merz said some parts were plausible and some understandable, but other elements were unacceptable from a European point of view.
He rejected the idea that the US needed to "save democracy" in Europe, saying Europeans could address such questions themselves.
The strategy also followed similar rhetoric to Trump's speech to the UN earlier this year, where he had harsh criticism for western Europe and its approach to migration and clean energy.