The Kremlin on Monday said that President Vladimir Putin was still "open" to speaking to Donald Trump after the US president said he was "very angry" with the Russian leader over little progress on a ceasefire in Ukraine.

Trump earlier criticised both Putin and Ukraine's Volodymyr Zelensky, as he pushes to end more than three years of conflict in Ukraine.

Trump told NBC he was "pissed off" at Putin for questioning Zelensky's credibility as someone to negotiate with and for calling for new authorities in Ukraine.

"The president remains open to contact with President Trump," Kremlin spokesman Dmitry Peskov told reporters in a briefing call.

He said there was no phone call scheduled between the two leaders, but that one could be "organised promptly" if deemed "necessary".

Putin earlier this month rejected a US proposal of an unconditional ceasefire in Ukraine, that Zelensky backed, and has upped his rhetoric on Moscow wanting to install new leadership in Ukraine.

"We are continuing work.. Firstly, on developing bilateral relations and also working on implementing some ideas, linked to resolving the Ukrainian (conflict)," Peskov said.

"Work is ongoing. There is nothing concrete yet. This process is time-consuming, probably due to the fact of the complexity of the substance," he added.

On Sunday, NBC News journalist Kristen Walker said Trump had called her to say he was angry with Putin and threatened tariffs on firms dealing with Russian oil.

Trump later said he was "disappointed" with Putin for his comments on Zelensky.

"He's supposed to be making a deal with him, whether you like him or you don't like him," Trump said. (AFP)