Ukrainians on Saturday laid flowers to honour their dead, wept, and hoped for victory despite the war's mounting toll, as they marked two years since a full-scale Russian invasion that shows no sign of letting up.

In the capital Kyiv, where President Volodymyr Zelensky led commemorative events alongside visiting foreign leaders, some feared the war would last years.

"I'm a realist and understand that most likely the war will drag on for the next three or four years. I hope society will mobilise, I hope we'll be able to somehow defeat Russia," said Denys Symonovskiy, a Kyiv resident.

In the western city of Lviv, hundreds of kilometres from the fighting, women cried as a priest led prayers in a cemetery festooned with blue-and-yellow Ukrainian flags, each marking the death of a soldier.

"The boys are holding the front line. We can only imagine what effort and price is paid for every peaceful day we have. I want to believe it's not all in vain. We have funerals every day," said Evhenia Demchuk, a widow and mother of two.

"We believe victory will be ours. It is all obtained at a very high price."

As the war enters its third year, Russian forces hold around 18% of Ukraine's land mass and are mounting new offensives in the east, buoyed by the capture of the ruined town of Avdiivka last weekend.

Exhausted by two years of fighting, Ukraine's government faces numerous challenges, not least regenerating battlefield manpower without wrecking the fragile economy.

Kyiv is also critically short of artillery rounds as U.S. Republicans hobble White House attempts to supply new military assistance to help Ukraine resist a much bigger and better armed foe.

UKRAINIANS LEARNING TO LIVE IN 'CONSTANT DANGER'

For most Ukrainians, the shock of the invasion has long given way to ever-present fear, even for residents of Kyiv, which is far from the fighting and well covered by air defences.

"I would say it has totally changed my life ... I went to sleep in one life and I woke up in a totally different life," said Oleh Papushenko, an English-language teacher out in central Kyiv.

"(The war) ruined a lot of lives, it took a lot of lives. But for me, it's just a constant danger of being killed by Russian missiles or a fear of being occupied by those ... animals."

Olha Kyrylenko, a Kyiv journalist who wrote about society and politics before the war, said her boyfriend was fighting at the front and that the war now dominated her life.

"Most of my friends are either fighting or volunteering for the army. That's it. Now, each day of this life is war."

As memorial events took place across the country, the war raged on.

Paramedics carried a wounded Ukrainian soldier covered in blood to a bed to undergo surgery in a "stabilisation point" near the front lines in the Donetsk region, which is partially occupied by Russian forces.

"We're forever grateful to you, sunshine," a female medic told him.

Captain Oleh Tokarchuk, commander of the medical unit for the 10th Separate Mountain Assault Brigade, said fighting was becoming more intense.

"Now we have on average about 30 wounded a day, these are not small numbers," he said, not that the figure was almost twice what had been in autumn.

"One thing I can say: whatever the intensity of the fighting, there hasn't been a single day without a wounded soldier over the past year."

He said the war was taking Ukraine's best and brightest, and that up to 90% of the injuries were caused by drones.

"They could be creating something, building something, doing business, developing our country. Instead, they are being killed or wounded ... these are grave losses for our country."