US President Donald Trump (L) and Russian President Vladimir Putin shake hands during a joint press conference after their summit on July 16, 2018 in Helsinki, Finland. (Photo by Chris McGrath/Getty Images) 
Russia has pounded Ukrainian energy installations and its electricity grid throughout the war, and Kyiv has responded with damaging strikes on refineries and fuel depots.
If implemented, Tuesday's agreement would represent a genuine de-escalation in the three-year war. The Kremlin made no mention of Ukraine's specific stance on the temporary halt in the targeting of energy infrastructure, but said Trump's proposal had spoken of "a mutual refusal."
The agreement fell short however of a wider agreement that the U.S. had sought, and which was accepted by Ukraine, for a blanket 30-day truce in the war.
"During the conversation, Donald Trump put forward a proposal for the parties to the conflict to mutually refrain from striking energy infrastructure facilities for 30 days. Vladimir Putin responded positively to this initiative and immediately gave the Russian military the corresponding command," the Kremlin said in a statement.
On the proposed wider truce Putin reiterated concerns that he had raised last week, according to the Kremlin's readout.
"The Russian side outlined a number of significant points regarding ensuring effective control over a possible ceasefire along the entire line of combat contact, the need to stop forced mobilisation in Ukraine, and the rearming of the Ukrainian Armed Forces," it said.
Putin also said that the key condition for resolving the conflict diplomatically should be "the complete cessation of foreign military assistance and provision of intelligence information to Kyiv", the Kremlin added.
It said Putin had questioned Ukraine's willingness to negotiate in good faith, and had accused it of carrying out "barbaric terrorist crimes" during a seven-month incursion into Russia's western Kursk region.
Ukraine denies such atrocities, and similarly questions Russia's trustworthiness and whether Moscow would respect any deal.
The Kremlin said the conversation between Putin and Trump had been a "detailed and frank exchange of views."
It said Putin had underlined that a resolution of the conflict must be "comprehensive, sustainable and long-term" and take into account Russia's own security interests and the root causes of the war.
Putin, it said, had also "responded constructively" to a Trump initiative on protecting shipping in the Black Sea and the two sides agreed to begin negotiations.
The Kremlin said that Russia and Ukraine would conduct another prisoner exchange on Wednesday, trading 175 people from each side.
Putin has said he wants Ukraine to drop its ambitions to join NATO, Russia to control the entirety of the four Ukrainian regions it has claimed as its own, and the size of the Ukrainian army to be limited.
He has also made clear he wants Western sanctions eased and a presidential election to be held in Ukraine, which Kyiv says is premature while martial law is in force.
(Reporting by Reuters, writing by Mark TrevelyanEditing by Andrew Osborn)