That, he added, would allow US-Russia ties to be fully restored, with Putin supporting the US president's view.
The call, which the Kremlin said lasted an hour, followed a weekend visit to Moscow and Kyiv by American envoys Steve Witkoff and Jared Kushner.
Ushakov told reporters that Trump had made it clear he wanted the war quickly finished.
"Donald Trump clearly emphasised the desirability of bringing the conflict to an end as soon as possible, which would immediately open up prospects – impressive and far-reaching ones at that – for the full restoration of relations between the US and Russia," Ushakov said, quoted by the Reuters news agency.
"In his view, this would have a particular impact on trade and economic ties, promising enormous benefits for both countries."
During the call, Putin and Trump also reviewed last weekend's visits by Witkoff and Kushner.
Trump reportedly proposed restoring normal US-Russia relations during his term, an idea Putin welcomed.
The two leaders also discussed a possible prisoner exchange.
Ushakov described the conversation as constructive and said the two presidents had agreed to stay in touch and would call each other again if the need arose.
Addressing speculation about Russian hostility towards European states, Ushakov said: "It was emphasised that we have absolutely no aggressive plans whatsoever towards Europe."
(ał)
Source: PAP, Reuters