“We will assume that the Ukrainian side will follow our example,” Mr. Putin said in a meeting televised on Saturday with his top military commander, Gen. Valery V. Gerasimov.

Mr. Putin claimed that Kyiv’s response would shed light on Ukraine’s “desire, and, indeed, its ability” to take part in negotiations to end the war.

The offer seemed designed to do two things: Appeal to President Trump and put President Volodymyr Zelensky of Ukraine into a bind. He could reject the truce offer and risk angering Mr. Trump. Or he could take it, and risk letting Russia take advantage of a planned cessation in hostilities to gather its forces for a new push.

Mr. Zelensky tried to thread the needle. He said Ukraine would abide by a truce so long as Russia did. And if Russia kept fighting, so would Ukraine.

“If Russia is now suddenly ready to truly engage in a format of full and unconditional silence, Ukraine will act accordingly — mirroring Russia’s actions,” Mr. Zelensky said in a social-media post. “Silence in response to silence, defensive strikes in response to attacks.”

Air-raid sirens rang out in Kyiv, Ukraine’s capital, around 5 p.m. local time, shortly after Mr. Putin announced the cease-fire and an hour before it was due to start. An hour after the truce was set to begin, Andriy Kovalenko, a Ukrainian defense official, said that “the Russians continue to fire in all directions, as before. Most of all in the East.”

More than two hours later, Mr. Zelensky said that Russian assaults continued in several places along the front, and that Russian artillery fire hadn’t subsided. Shortly later, at about 10 p.m. local time, another air-raid alert rang out in Kyiv.

In his initial response to the truce offer, Mr. Zelensky referred to the offer of a truce as Mr. Putin’s “next attempt to play with people’s lives.” “Ukrainian air defense and aviation have already begun working to defend themselves,” he added. Referring to Iranian-designed Russian drones, he went on: “Russian ‘Shaheds’ in our skies are Putin’s true attitude to Easter and to people’s lives.”

Ukraine’s foreign minister, Andrii Sybiha, said on X Saturday evening that Mr. Putin could not be trusted, suggesting that Russia could sign on to a 30-day cease-fire proposal that Mr. Trump had proposed in March and Ukraine had already agreed to. “We will look at actions, not words,” he wrote.

Mr. Zelensky added that if a complete truce took hold over the Easter holiday, Ukraine wanted to extend it, adding that 30 hours was not enough for “for genuine confidence-building measures.” He said: “Thirty days could give peace a chance.”

Russia previously declared a unilateral truce for the Eastern Orthodox Christmas in January 2023. At the time, Mr. Zelensky dismissed the idea as cynical posturing meant to allow Russia to reposition soldiers and equipment.

The Kremlin also quickly sought to turn Washington’s attention to Mr. Putin’s announcement. Kirill Dmitriev, an envoy for Mr. Putin who traveled to Washington this month, posted the news on X, adding, “One step closer to peace” and an emoji of a dove.

Mr. Putin’s move came a day after the Trump administration made its impatience plain with Russia’s unwillingness to agree to the 30-day cease-fire.

Secretary of State Marco Rubio said on Friday that the United States could decide “in a matter of days” to “move on” from trying to end the war. Mr. Trump said later that “if for some reason one of the two parties makes it very difficult,” the United States could decide that “we’re just going to take a pass.”

On Saturday evening, in another sign that both Ukraine and Russia were trying to show positive movement on the war, the countries exchanged the largest number of prisoners of war in a single swap since Russia launched its full-scale invasion in February 2022. Mr. Zelensky said that 277 Ukrainian soldiers had returned home in time for Easter. Officials said 246 Russian soldiers also were sent home.

In his televised meeting on Saturday with General Gerasimov, Mr. Putin sought to portray Russia as seeking peace and Ukraine as the recalcitrant party. He said Russian forces needed to be ready “to repel possible cease-fire violations and provocations by the enemy.”

“We have always been ready” for peace talks, Mr. Putin said.

Easter is an important holiday in both Russia and Ukraine, but many Ukrainians expressed immediate skepticism that Russian forces would stop attacking. Bogdan Butkevych, a Ukrainian journalist and radio DJ, said on Facebook that he believed the offer meant more killing would come.

Referring to the Chinese leader, Xi Jinping, and the informal club of nations that also includes Brazil, India and South Africa, Mr. Putin added that Russia welcomed “in every way the efforts of President Trump, our Chinese friends, the chairman of the People’s Republic of China, the BRICS countries and all supporters to achieve a fair and peaceful settlement of the Ukraine crisis.”

“The goal is to provoke us into responding,” he wrote. “Don’t even think about relaxing or believing this.”