The two leaders spoke at a joint press conference after meeting at Trump's Mar-a-Lago resort in Florida.
Trump said it will be clear "in a few weeks" whether negotiations to end the war will succeed.
Zelenskiy thanked the US president for a "really great discussion" and said American and Ukrainian teams would meet next week to finalise issues aimed at ending Russia's war in Ukraine.
"We had a substantive conversation on all issues and highly value the progress that the Ukrainian and American teams have made over the past weeks," he said in a statement on the Telegram messaging app.
Zelenskiy said an agreement on security guarantees for Ukraine had been reached.
Trump was slightly more cautious, saying that they were 95 per cent of the way to such an agreement, and that he expected European countries to "take over a big part" of that effort with US backing.
Zelenskiy has said previously that he hopes to soften a US proposal for Ukrainian forces to withdraw completely from the Donbas region of eastern Ukraine, a Russian demand that would mean ceding some territory held by Ukrainian forces.
Trump and Zelenskiy said the future of the Donbas had not been settled.
"It's unresolved, but it's getting a lot closer. That's a very tough issue," Trump said.
Just before Zelenskiy and his delegation arrived in Florida, Trump and Russian President Vladimir Putin spoke in a call described as "productive" by the US president and "friendly" by Kremlin foreign policy aide Yuri Ushakov.
Ushakov, in Moscow, said Putin told Trump a 60-day ceasefire proposed by the European Union and Ukraine would prolong the war.
The Kremlin aide also said Ukraine needs to make a decision regarding the Donbas "without further delay."
And he said the Russian government had agreed to establish working groups to resolve the conflict that will focus on economic and security concerns.
Zelenskiy arrived at Mar-a-Lago on Sunday afternoon, as Russian air raids pile pressure on Kyiv.
Russia hit the capital and other parts of Ukraine with hundreds of missiles and drones on Saturday, knocking out power and heat in parts of Kyiv. Zelenskiy has described the weekend attacks as Russia's response to the US-brokered peace efforts, but Trump said he believes Putin and Zelenskiy are serious about peace.
The US president said he will call Putin again after meeting with Zelenskiy. Zelenskiy had previously told journalists he plans to discuss the fate of the contested Donbas region with Trump, as well as the future of the Zaporizhzhia nuclear power plant and other topics.
Putin said Moscow would continue waging its war if Kyiv did not seek a quick peace. Russia has steadily advanced on the battlefield in recent months, claiming control over several more settlements on Sunday.
While Kyiv and Washington have agreed on many issues, the issue of what territory, if any, will be ceded to Russia remains unresolved. While Moscow insists on getting all of the Donbas, Kyiv wants the map frozen at current battle lines.
The US, seeking a compromise, has proposed a free economic zone if Ukraine leaves the area, although it remains unclear how that zone would function in practical terms.
with DPA
