Rescuers in Ukraine searched through rubble Saturday after Russian strikes killed at least 39 people the day before, one of the fiercest attacks since the early days of the war.

Schools, a maternity hospital, shopping arcades and blocks of flats were among the buildings hit in Friday's barrage, Ukrainian officials said.

The strikes - during which a Russian missile passed through Polish airspace - triggered international condemnation and fresh promises of military support to Ukraine, which has been fighting off invading Russian troops since late February 2022.

Ukraine's military estimated Russia had launched 158 missiles and drones on Ukraine and 114 of them had been destroyed.

Air force spokesman Yuriy Ignat told AFP that this was a "record number" of missiles and "the most massive missile attack" of the war, excluding the early days of constant bombardment.

Russia tried to overwhelm Ukraine's air defences across most major cities, launching a wave of Shahed attack drones followed by missiles of numerous types fired from planes and from Russian-controlled territory.

At least 39 people were killed in Friday's strikes, Ukrainian President Volodymyr Zelensky said.

"Work is still underway to eliminate the consequences of yesterday's Russian attack," he wrote in a post on social media Saturday.

"In total, 159 people were injured in this terrorist attack. Unfortunately, 39 of them have been killed so far," he said.

January 1 will be declared a day of mourning in the capital Kyiv, where at least 16 people were killed, Mayor Vitali Klitschko said.

'Stop this terror'

Russia's army said it had "carried out 50 group strikes and one massive strike" on military facilities in Ukraine over the past week, adding that "all targets were hit".

The United Nations condemned the attacks and said they must stop "immediately".

Poland reported that a Russian missile passed through its airspace.

"Everything indicates that a Russian missile entered Polish airspace... It also left," said General Wieslaw Kukula, chief of the general staff of the Polish armed forces.

After speaking to Polish President Andrzej Duda, NATO chief Jens Stoltenberg said the alliance "stands in solidarity" with Poland, adding: "NATO remains vigilant."

In the face of sustained Russian assaults, Ukraine is urging Western allies to maintain military support.

Ukraine presidential aide Andriy Yermak said Kyiv needed "more support and strength to stop this terror".

US President Joe Biden called on Congress to overcome its division to approve new aid for Ukraine, after Washington released its final package of weaponry under existing agreements still to be renewed by Congress.

"Unless Congress takes urgent action in the new year, we will not be able to continue sending the weapons and vital air defence systems Ukraine needs to protect its people," Biden said.

"Congress must step up and act without any further delay."

Britain announced it would send hundreds more air defence missiles to Kyiv, after Prime Minister Rishi Sunak declared that "We must continue to stand with Ukraine - for as long as it takes".

Maternity ward 'severely damaged'

The strikes targeted at least six Ukrainian regions including Kharkiv in the northeast, Lviv in the west, Dnipro in the east and Odesa in the south.

In Dnipro, a maternity hospital was "severely damaged" but staff and patients managed to shelter in time, the health ministry said.

There were 12 women in labour and four newborns inside when it was struck, governor of the Dnipropetrovsk region, Sergiy Lysak, said on Friday.

Lysak also reported six killed and 28 wounded in strikes on a shopping mall, private houses and administrative buildings.

Kharkiv faced around 20 strikes, which killed three employees at a civilian enterprise and wounded 11, governor Oleg Synegubov said on Friday.

In Zaporizhzhia, on the shores of the Dnipro river, governor Yuriy Malashko reported seven dead and 13 wounded according to a Friday toll.

In the Odesa region, which has seen renewed attacks since the summer, four people were killed.

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Strikes over Lviv in western Ukraine are much more rare, but the region was not spared on Friday.

One person was killed and 15 wounded as blocks of flats and two schools were damaged, the interior ministry said.

Separately, local Russian officials said Saturday at least four people including three children were killed by Ukrainian strikes in the border regions of Belgorod and Bryansk over the past 24 hours.

Belgorod is about 30 kilometres (19 miles) from the border with Ukraine and has been repeatedly targeted by what Russia says is indiscriminate shelling by Kyiv's forces.