The conversation between the two was the first known in over two weeks, and was announced by both the Kremlin and the White House with a few hours' notice.
Putin's comments were relayed by a close associate in the Kremlin, reports AFP.
Putin is said to have stated that he is willing to resume the talks led by emissaries from the US in Turkey.
Exchange of prisoners of war
The indirect talks led to exchanges of prisoners of war and the dead. Russia has stood firm on, among other things, territorial demands in Ukraine - but rejected proposals for a ceasefire. Something that seems to have been repeated during Thursday's conversation with Trump.
The White House has not yet commented on the discussion, in which the development in the Middle East was also discussed, and where Putin wanted to see "a diplomatic solution", according to the Kremlin.
According to the Kremlin's spokesperson, Trump is said to have demanded a swift end to the Russian invasion war in Ukraine.
At the same time, a telephone conversation between Trump and Ukraine's President Volodymyr Zelenskyj is being prepared, which is likely to take place on Friday, according to a high-ranking Ukrainian source.
Doubtful Zelenskyj
At a press conference in Denmark on Thursday, Zelenskyj states that he does not really know what the telephone conversation between Donald Trump and Vladimir Putin can lead to. But he repeats what he wants to see.
- We have said from the beginning that we are ready for all types of meetings. In Russia, Putin is the only real decision-maker. Therefore, we need a meeting at the highest level, if we really want peace, says Zelenskyj.
Zelenskyj was in Denmark to meet King Fredrik, Prime Minister Mette Frederiksen and the EU's Ursula von der Leyen.
