The two sides said the ceasefire would go into effect on October 27, allowing the delivery of aid and the evacuation of residents through humanitarian corridors.
Amid a US push to organise new talks aimed at ending the four-and-a-half-year-old war, Zelenskiy said negotiators from Ukraine, Russia and the United States had agreed to technical-level meetings in the first half of November in Abu Dhabi.
A US official later said the three countries might hold their next talks in a couple weeks in Abu Dhabi or Switzerland.
Zelenskiy said he hoped a meeting of the countries' leaders would follow.
Previous talks headed by the United States stalled in February with no significant progress towards ending the bloodiest conflict in Europe since World War II.
Russia continues to demand Ukraine cede all of the eastern Donbas region, including territory Russia has not occupied militarily, while Kyiv rejects any notion of giving up land it holds.
The latest peace efforts follow a rift between Washington and Kyiv in recent weeks and moves by US President Donald Trump seen as favouring Russia.
A major source of friction was limitations placed on SpaceX's Starlink communication system that Ukraine uses to protect against incoming attacks.
Trump said that if Ukraine still faced a problem with the system, he would straighten it out and, if necessary, speak to SpaceX CEO Elon Musk.
Another contentious point was Trump's announcement of a deal to allow Russia to provide diesel for the US and global markets, an agreement denounced by Ukraine and meant to keep prices down as the president's Republicans contest US midterm elections.
On Friday, Russian Deputy Prime Minister Alexander Novak said the first three tankers with Russian diesel were on their way to North America.
In the town of Oleshky, occupied by Russian forces since February 2022, residents have reported that they faced a deepening food crisis.
"Both nations agreed to temporarily stop all military action in Oleshky to allow for humanitarian aid to enter and to prepare a civilian evacuation through a designated safe passageway," the White House said in a statement.
Both sides said Melania Trump played an important role in co-ordinating the agreement.
The first lady has been active in trying to get Ukrainian children seized by Russia during the war returned to their families.
"Oleshky is a frontline war city on the brink of disaster," she said in a statement, with the remaining population urgently needing food, clean water and medical attention.
The White House said Oleshky, across the Dnipro River from the Ukrainian-held city of Kherson, had 1700 to 2000 residents remaining, down from 24,000 before the war.
Zelenskiy's comments on resuming peace talks followed a meeting with US presidential envoy Steve Witkoff in Norway this week and a subsequent meeting between Witkoff and President Vladimir Putin in St Petersburg.
"The plan is to meet in the first half of November, and as early as possible, of course," Zelenskiy told the Hudson Institute think tank via a video link.
He said much would depend on Russia, noting that a similar meeting expected in October had not materialised.
Ukrainian officials said on Friday that speed restrictions on Starlink systems in Ukraine remained in place, despite Trump's previous statement that the services had been fully restored.
Trump told reporters at the White House on Friday that he had not spoken to Musk about the restrictions but would do so if required.
"If there is a problem, I'll get it straightened out," he said.
The caps have been in place since October 13.
