Kyrylo Tymoshenko, the deputy head of President Volodymyr Zelenskiy's office, said the evacuation effort was stopped because the city of Mariupol remained under fire on Saturday.
"The Russian side is not holding to the ceasefire and has continued firing on Mariupol itself and on its surrounding area," he said.
"Talks with the Russian Federation are ongoing regarding setting up a ceasefire and ensuring a safe humanitarian corridor."
The Russian defence ministry said earlier in a statement it had agreed on humanitarian corridor routes with Ukrainian forces for Mariupol, a strategic port in the southeast, and for the eastern city of Volnovakha.
Russia breached the deal in Volnovakha as well, Deputy Prime Minister Iryna Vereshchuk told reporters.
"We appeal to the Russian side to stop firing," she said.
The Russian defence ministry said that the firing came from inside both cities against Russian positions.
The struggle to enforce the ceasefire showed the fragility of efforts to stop fighting across Ukraine as people continued to flee the country on the 10th day after Russian forces invaded.
"We are doing everything on our part to make the agreement work," Zelenskiy said.
"This is one of the main tasks for today. Let's see if we can go further in the negotiation process."
Mariupol had been the scene of growing misery in recent days amid an assault that knocked out power and most phone service and raised the prospect of food and water shortages for hundreds of thousands of people in freezing weather.
Pharmacies are out of medicine, Doctors Without Borders said.
A top official in Mariupol, Pavlo Kirilenko, the head of the Donetsk military-civil administration that includes the city, had said the humanitarian corridor would extend to Zaporizhzhia, 226km away.
In comments carried on Ukrainian television, Mariupol Mayor Vadym Boychenko said thousands of people had gathered for safe passage out of the city and buses were departing when shelling began.
"We value the life of every inhabitant of Mariupol and we cannot risk it, so we stopped the evacuation," he said.
Before Russia announced the limited ceasefire, Ukraine had urged Russia to create humanitarian corridors to allow children, women and the older adults to flee the fighting, calling them "question No 1".
Aeroflot, Russia's flagship state-owned airline, announced that it plans to halt all international flights except to Belarus, starting on Tuesday amid sanctions imposed on Russia.
The country's aviation agency, Rosaviatsiya, had recommended that all Russian airlines with foreign-leased planes halt passenger and cargo flights abroad to prevent the aircraft from being impounded.
As Russian forces batter strategic locations in Ukraine, Zelenskiy has lashed out at NATO for refusing to impose a no-fly zone over his country, warning that "all the people who die from this day forward will also die because of you".
NATO has said a no-fly zone, which would bar all unauthorised aircraft from flying over Ukraine, could provoke widespread war in Europe with nuclear-armed Russia.
But as the United States and other NATO members send weapons for Ukraine and more than one million refugees spill through the continent, the conflict is already drawing in countries far beyond Ukraine's borders.
Russia continues to crack down on independent media reporting on the war, also blocking Facebook and Twitter, and more outlets say they are pausing their work inside the country.
In a video message to anti-war protesters in several European cities, Zelenskiy appealed for help.
"If we fall, you will fall," he said.
The United Security Council scheduled an open meeting for Monday on the worsening humanitarian situation.
The UN estimates that 12 million people in Ukraine and four million fleeing to neighbouring countries in the coming months will need humanitarian aid.
13°C