Before the overnight attacks, Zelenskiy said his talks in Florida on Sunday would focus on the territory to be controlled by each side after a halt to the fighting that began in February 2022 with President Vladimir Putin's invasion of Russia's smaller neighbour, Europe's deadliest conflict since World War II.
Explosions sounded in Kyiv as Ukraine's air defence units went into action, and the military said on the Telegram messaging app that missiles were being deployed. The air force said Russian drones were targeting the capital and regions in the northeast and south.
An air raid alert remained in effect in the capital on Saturday, some four hours after being introduced. There were no immediate reports of damage or power cuts.
Russia made no immediate comment on the attacks.
On Thursday night, Russia struck Ukraine's energy infrastructure and stepped up attacks on the southern region of Odesa, the site of Ukraine's main seaports.
Amid the continued fierce fighting, territory remains the main diplomatic stumbling block. A 20-point draft in the US-driven campaign to clinch a peace plan is 90 per cent complete, Zelenskiy told journalists in Kyiv.
He said a security guarantee agreement between Ukraine and the US was almost ready - a key element after guarantees in earlier post-Soviet years proved meaningless.
"A lot can be decided before the New Year," Zelenskiy posted on social media.
Trump said the United States was the driving force behind the process.
"He doesn't have anything until I approve it," Trump told Politico. "So we'll see what he's got."
Zelenskiy told Axios the US had offered a 15-year deal on security guarantees, subject to renewal, but Kyiv wanted a longer agreement with legally binding provisions to guard against further Russian aggression.
Trump said he believed Sunday's meeting would go well. He also said he expected to speak with Putin "soon, as much as I want".
In addition to territory, a critical point is control of the Zaporizhzhia nuclear power station, Europe's largest, seized by Russia in the opening weeks of the war.
Moscow demands that Ukraine withdraw from the areas of the eastern region of Donetsk that Russian troops have failed to occupy in their drive to secure all of the Donbas, which also includes the Luhansk region.
Kyiv wants the fighting halted at the current lines.
Under a US compromise, a free economic zone would be set up if Ukraine leaves parts of the Donetsk region, though details have yet to be worked out.
Axios quoted Zelenskiy as saying that if he is not able to push the US to back Ukraine's "strong" position on the land issue, he was willing to put the 20-point plan to a referendum - as long as Russia agrees to a 60-day ceasefire to allow Ukraine to prepare for and hold the vote.
He said he wanted more pressure applied to Russia.
Russian Deputy Foreign Minister Sergei Ryabkov said Kyiv's version of the 20-point plan differed from what Russia had been discussing with the US, according to Interfax-Russia news agency.
But he expressed optimism that matters had reached a "turning point" in the search for a settlement.
Putin's foreign policy aide, Yuri Ushakov, spoke with members of the Trump administration after Moscow received US proposals about a possible peace deal, the Kremlin said on Friday. It did not disclose how Moscow had viewed the documents.
