Diplomatic efforts to end Russia's all-out invasion of Ukraine have stalled in recent months, in part because the United States has shifted its focus towards the Iran war.
Russia fired hundreds of drones at Ukraine on Wednesday, killing at least five people and destroying a postal terminal, Ukrainian officials said.
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The attacks came a day after the Kremlin rejected a Ukrainian proposal for a temporary ceasefire over Easter.
Ukrainian President Volodymyr Zelenskyy said Wednesday he had had a "positive" call with US negotiators Steve Witkoff and Jared Kushner about reviving the peace process.
Diplomatic efforts to end Russia's full-scale invasion of Ukraine, now in its fifth year, have stalled in recent months, in part because the United States has shifted its focus towards the Iran war.
The two sides had agreed to "strengthen security guarantees", he added.
"Ukraine is doing everything it can to support efforts for peace," Zelenskyy said in his evening address.
NATO chief Mark Rutte and US Senator Lindsey Graham also took part in the call, Zelenskyy said.
Zelesnkyy's remarks came after Russian drones damaged sites in western Ukraine near the Polish border early on Wednesday, including an industrial facility in the city of Lutsk, some 400 kilometres west of Kyiv.
Ukraine's Nova Poshta mailing company published an image showing a warehouse in Lutsk in flames following a Russian attack, thick smoke pouring from its roof.
Mayor Ihor Polishchuk said a postal sorting centre and a food distribution site were damaged, and falling drone debris also set a residential building on fire.
Russia fired 339 drones at Ukraine overnight, and more than 360 drones during the day, according to the Ukrainian air force.
A Russian drone killed four people in the central Cherkasy region. An earlier drone strike on a car in Ukraine's frontline Kherson region killed a woman and badly wounded two other people, regional authorities said.
Meanwhile, Russia also stepped up pressure on the front line, claiming on Wednesday to have taken two villages in eastern Ukraine and fully occupied the Luhansk region, a claim which cannot be independently verified.
Zelenskyy described the situation on the front as "quite tense" in an earlier social media post.