Trump said the United States could own and run Ukraine's nuclear power plants, the latest in a series of proposals he has made to the war-torn country, reliant on Washington's support to fend off the Russian invasion.

"We will not discuss it. We have 15 nuclear power units in operation today. This all belongs to our state," Zelensky told a news conference in Oslo, where he held talks with Norway's Prime Minister Jonas Gahr Store.

He said the nuclear plants legally belonged to the Ukrainian people but that Kyiv was open to US investment once Ukraine got back control of the Zaporizhzhia plant, seized by Russian troops at the start of the war.

"If they want to take it back from the Russians, if they want to modernise it, invest -- this is a different question, this is an open question, we can talk about it," Zelensky added.

Trump made the proposal during a call with Zelensky on Wednesday, which was believed to be their first conversation since a blazing televised row in the Oval Office last month.

Trump's tone on Wednesday was positive after the Zelensky call, during which he "discussed Ukraine's electrical supply and nuclear power plants" according to a statement from National Security Advisor Mike Waltz and Secretary of State Marco Rubio.

"American ownership of those plants would be the best protection for that infrastructure," the statement said.