Dozens of buses tightly packed with exhausted evacuees from Mariupol and other Russian-occupied cities in southeast Ukraine arrived in Zaporizhzhia Friday to the relief of waiting relatives, according to an AFP reporter on the scene.

The passengers included people who managed to flee besieged Mariupol, as well as residents of Berdiansk and nearby Melitopol.

As the coaches pulled into a shopping centre on the outskirts of Zaporizhzhia more than 200 kilometres (120 miles) northwest, some evacuees wept with relief to be back in Ukrainian-controlled territory.

"We were crying when we reached this area. We were crying when we saw soldiers at the checkpoint with Ukrainian crests on their arms," said Olena, who carried her young daughter in her arms.

"My house was destroyed. I saw it in photos. Our city doesn't exist anymore."

Mariupol has suffered near-total destruction since Russia's invasion of Ukraine, leaving residents without food, water and heat as they endured heavy bombardment.

On Friday, the International Committee of the Red Cross said its rescue convoy had been forced to turn back after it became "impossible to proceed". It said it would try another evacuation attempt Saturday.

An estimated 160,000 people are believed to still be trapped in the southeastern port city after several evacuation attempts collapsed, though some have made the dangerous dash to freedom alone.

In a video address posted on Telegram, Deputy Prime Minister Iryna Vereshchuk confirmed Friday that 42 buses from Berdiansk had successfully brought people to safety, including Mariupol residents. Another 771 Mariupol residents had found their own transportation to Zaporizhzhia, she added.

"Know and believe: we are with you," Vereshchuk said.

Later, President Volodymyr Zelensky said they had "managed to rescue 6,266 people, including 3,071 people from Mariupol", though it was not immediately clear if he was talking about the people on the buses.

Several evacuees from Mariupol told AFP they had to walk 15 kilometres or more to escape the city, before locating private vehicles to continue their journey.

Once they reached Russian-occupied Berdiansk, some were stranded for a further two weeks after several unsuccessful attempts to leave.

Their journey ended with a 12-hour bus ride that snaked its way through a series of checkpoints before arriving in Zaporizhzhia, a trip that would have taken just three hours before the war.

With no bathrooms onboard, some people had wet themselves, while other passengers were in desperate need of medication, such as insulin.

After the convoy arrived, an elderly woman from Mariupol grasped at the sky as she was transferred to a stretcher and rushed to hospital. Doctors said she had suffered a stroke.

Waiting outside during the post-curfew blackout, Ludmilla wept tears of joy when she spotted her mother's face through the window of one of the first buses to arrive.

"Three days ago my mother walked out of Mariupol and then found a car to take her to Berdiansk. I can't tell you how I feel to see her here," said Ludmilla, who left Mariupol on March 12 with husband Nikita.

Olga also anxiously waited to find family members on the buses.

"There are no words for how happy I am to see she is safe."

"Her mother's family are still in Mariupol and we don't know if they are alive," she added.