More than 1.5 million people have fled Ukraine since the Russian invasion began, the head of the U.N. Refugee Agency said on Sunday.

"More than 1.5 million refugees from Ukraine have crossed into neighbouring countries in 10 days -- the fastest growing refugee crisis in Europe since World War II," Filippo Grandi, the U.N. high commissioner for refugees, said on Twitter.

An official in Mariupol, a Ukrainian city besieged by the Russians, said a cease-fire on Sunday will allow citizens to evacuate.

The temporary cease-fire was scheduled to begin at 10 a.m. local time, with an evacuation starting two hours later, Pavlo Kyrylenko, governor of Donetsk Oblast, said on Facebook.

A similar plan had been announced for Saturday, but Russian shells continued to fall throughout the day.

The World Health Organization said on Sunday it had confirmed "several" attacks on health care facilities in Ukraine.

The attacks caused "multiple deaths and injuries," WHO Director-General Tedros Adhanom Ghebreyesus said on Twitter.

"Additional reports are being investigated," he said. "Attacks on healthcare facilities or workers breach medical neutrality and are violations of international humanitarian law."

Ukraine’s military on Sunday said it was "fighting fierce battles to maintain certain borders," including defending Chernihiv and Mariupol, cities targeted by Russian shelling.

"The enemy, suffering losses, makes constant attempts to avoid direct fire contact with our troops," military officials said, according to an official translation posted on Facebook.

An operation is underway to defend Chernihiv, a city about 100 miles north of Kyiv, the capital, the update said. In the east, the Ukrainian military’s "main efforts are focused on defending the city of Mariupol and inflicting fire damage on the overwhelming forces of the enemy."

Ukraine’s military claimed on Sunday to have destroyed 88 Russian aircraft and helicopters.

"Some enemy pilots who catapulted and survived were found by Ukrainian soldiers," the update said. "They have received medical treatment and are already testifying about the Putin regime's crimes against humanity."

The United Nations High Commissioner for Human Rights has "received credible reports of several cases of Russian forces using cluster munitions, including in populated areas," spokesperson Elizabeth Throssell said Friday.

"Due to their wide-area effects, the use of cluster munitions in populated areas is incompatible with international humanitarian law principles," Throssell said.

Throssell added, "We remind Russian authorities that directing attacks against civilians and civilian objects as well as so-called bombardment in towns and villages and other forms of indiscriminate attacks are prohibited under international law and may amount to war crimes."

To date, there have been 26 attacks on health care facilities in Ukraine, killing at least 12 people and injuring 34 people, according to Jašarević. Two of those killed and eight of the injured were healthcare workers.

That number is "shocking," said Throssell.

Throssell and WHO spokesperson Tarik Jašarević declined to pin the blame for all of them on Russia.

This number of attacks includes Wednesday's strike on a children's hospital and maternity ward in Mariupol. On Thursday, Russian officials claimed that the attack was staged, but they first confirmed they bombed it and claimed the hospital was being used by Ukrainian "radicals."

Throssell told reporters that is not true; "It was a functioning hospital," she said.

-ABC News' Conor Finnegan