It added that talks aimed at advancing toward a broader peace plan will begin "immediately," the Reuters news agency reported.
"Today, President Trump and President Putin spoke about the need for peace and a ceasefire in the Ukraine war," the White House said in a statement.
It added that both leaders "agreed this conflict needs to end with a lasting peace."
They also "stressed the need for improved bilateral relations between the United States and Russia," according to the statement.
"The blood and treasure that both Ukraine and Russia have been spending in this war would be better spent on the needs of their people," the White House also said. "This conflict should never have started and should have been ended long ago with sincere and good faith peace efforts.
Trump and Putin "agreed that the movement to peace will begin with an energy and infrastructure ceasefire, as well as technical negotiations on implementation of a maritime ceasefire in the Black Sea, full ceasefire and permanent peace," according to the statement.
"These negotiations will begin immediately in the Middle East," the White House announced.
Trump proposed a 30-day pause on attacks on energy infrastructure, and Putin "responded positively," the US political newspaper The Hill reported, citing Russian state media.
The White House also said in its statement that Trump and Putin "spoke broadly about the Middle East as a region of potential cooperation to prevent future conflicts."
They further discussed "the need to stop proliferation of strategic weapons and will engage with others to ensure the broadest possible application."
The two presidents "shared the view that Iran should never be in a position to destroy Israel," the White House added.
It concluded: "The two leaders agreed that a future with an improved bilateral relationship between the United States and Russia has huge upside. This includes enormous economic deals and geopolitical stability when peace has been achieved."
Trump told reporters before his phone call with Putin that negotiators working to end the Russia-Ukraine war had already discussed "dividing up certain assets."
The phone call between Trump and Putin came after Ukraine accepted a US-sponsored 30-day ceasefire plan during talks in Jeddah, Saudi Arabia, on March 11.
Russia launched a full-scale invasion of Ukraine on February 24, 2022, starting the largest military conflict in Europe since World War II.
Tuesday is day 1,118 of Russia's war on Ukraine.
(gs)
Source: IAR, PAP, Reuters, thehill.com