President Vladimir V. Putin of Russia agreed for the first time on Tuesday to a limited cease-fire that would stop strikes on energy infrastructure, as long as Ukraine does the same, the Kremlin said in a statement.

But in a two-and-a-half-hour phone call with President Trump, the Russian leader declined for now to agree to a broader 30-day halt in fighting that U.S. and Ukrainian officials had proposed, meaning that the attacks on Ukrainian civilians, cities and ports can continue as the two sides vie for territory.

Still, if strikes on energy infrastructure by both sides indeed stop, it would mark the first mutually agreed suspension of attacks in the three-year war, which the White House characterized as a first step toward a broader peace.

A cease-fire for energy targets would not only benefit Ukraine, which has struggled for years with Russia’s repeated attacks on its energy grid. It would also come as a relief to the Kremlin: Ukraine has conducted extensive strikes on oil and gas facilities deep into the Russian heartland, jeopardizing Moscow’s most crucial stream of state revenue.

President Volodymyr Zelensky of Ukraine said he was awaiting a phone call from Mr. Trump to find out the details of his discussion with Mr. Putin, but noted he was open to a truce on strikes targeting energy infrastructure.

“Russia and Ukraine, through the mediation of the U.S., can agree not to attack energy infrastructure,” he told the Ukrainian public broadcaster, Suspilne, Tuesday night. “Our side will support this. But it cannot be the case that Russia attacks our energy sector and we remain silent. We will respond.”

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