Zelenskiy held a call on Saturday with US President Donald Trump's special envoy Steve Witkoff and Trump's son-in-law Jared Kushner, and is expected to meet French, British and German leaders on Monday in London. Further talks are planned in Brussels.
"The American representatives know the basic Ukrainian positions," Zelenskiy said in his nightly video address. "The conversation was constructive, although not easy."
Trump has said ending Russia's war in Ukraine, now nearing its fourth year and the deadliest conflict in Europe since World War II, remains his toughest foreign policy challenge.
Despite US mediation and periodic high-level contacts, progress in the peace talks has been slow, with disputes over security guarantees for Kyiv and the status of Russian-occupied territory still unresolved.
The Kremlin welcomed a new US national security strategy, saying it was largely in line with Moscow's vision.
"There are statements there against confrontation and in favour of dialogue and building good relations," Kremlin spokesman Dmitry Peskov said, in comments published by Russia's Tass news agency.
The document released by the White House said the US wants to improve its relationship with Russia after years of Moscow being treated as a global pariah and that ending the war is a core US interest to "re-establish strategic stability with Russia."
Earlier, Zelenskiy called for allies to ramp up their support following massive air strikes by Russian forces.
Ukraine is continuing to work with its partners, "to ensure that, in response to these attacks, our defences grow stronger," Zelenskiy wrote on X.
"The priority is clear: more air defence systems and missiles, and more support for our defenders," he added, calling for every agreement to be implemented faster.
Russia again bombarded Ukraine over the weekend with multiple drone and missile strikes.
He said people were killed in Sloviansk in the east and in Chernihiv in the north while damage was reported in seven regions.
According to the Ukrainian Civil Defence, a 50-year-old man was killed in Novhorod-Siverskyi in the Chernihiv region and another person was killed in Sloviansk.
A 15-year-old was also injured in Sloviansk.
Zelenskiy wrote that the Russian military launched more than 240 drones and five ballistic missiles.
Overall this week, he said Russian forces deployed more than 1600 attack drones, about 1200 guided aerial bombs and almost 70 missiles of various types.
"The primary targets of these strikes are infrastructure that keeps everyday life going," he wrote.
with Reuters and AP
