Zelenskiy presented his war "victory plan" to Trump during a closed-door meeting on Friday after the Republican presidential candidate said he would work with both Ukraine and Russia to end their conflict.
The meeting between the two men at Trump Tower in Manhattan was their first in-person encounter since 2019.
Zelenskiy said he was talking with both Trump and Harris because Ukraine needed strong US support in its continuing war with Russia.
Vice President Kamala Harris has boarded a plane for the US-Mexico border. (AP PHOTO)
Trump praised Zelenskiy but said he also had a solid relationship with Russian President Vladimir Putin.
"We have a very good relationship (with Zelenskiy) and I also have a very good relationship, as you know, with President Putin," Trump told reporters.
"And I think if we win, I think we're going to get it resolved very quickly," he added.
Zelenskiy has used his visit to promote his "victory plan," which a US official described as a repackaged request for more weapons and a lifting of restrictions on the use of long-range missiles.
The plan presupposes the ultimate defeat of Russia in the war, the official said.
Some officials see the aim as unrealistic.
"It's an honour to have the president with us, and he's been through a lot," Trump said on Friday.
"He's been through a tremendous amount, like probably nobody else, almost nobody else in history if you really get right down to it, and we're going to have a discussion and see what we could come up with."
Trump on Friday said that if he won the November 5 election he would immediately begin working toward a resolution of the Ukraine conflict, even though he would formally take office only in late January 2025.
Zelenskiy met on Thursday with US President Joe Biden and Harris.
Harris on Friday will make her first visit to the US-Mexico border in three years to confront one of her biggest vulnerabilities ahead of the election.
She is scheduled to appear in Douglas, Arizona, as Trump and his fellow Republicans needle Harris relentlessly over the Biden administration's record on migration and fault the vice president for not visiting the border since June 2021 during her time in the White House.
Immigration and border security are top issues in Arizona, the only battleground state that borders Mexico and one that contended with a record influx of asylum seekers last year.
Trump has an edge with voters on migration, and Harris has gone on offence to improve her standing on the issue and defuse a key line of political attack for Trump.
In nearly every campaign speech she gives, Harris recounts how a sweeping bipartisan package aiming to overhaul the federal immigration system collapsed in Congress earlier this year after Trump urged top Republicans to oppose it.
"The American people deserve a president who cares more about border security than playing political games," Harris plans to say, according to an excerpt of her remarks previewed by her campaign.
After the immigration legislation stalled, Biden's administration announced rules that bar migrants from being granted asylum when US officials deem that the southern border is overwhelmed.
Since then, arrests for illegal border crossings have fallen.
Harris will also use her trip to remind voters about her work as attorney general of California in confronting crime along the border.
During an August rally in Glendale, outside Phoenix, she talked about helping to prosecute drug- and people-smuggling gangs that operated at the border.
"I prosecuted them in case after case, and I won," Harris said then.
Florida Democratic Representative Maxwell Frost, at 27 the youngest member of Congress, said that in backing stricter enforcement, Harris is trying to "strike a chord" and "she understands that, right now, there is a crisis at the border. It's a humanitarian crisis".
with AP
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