Ukraine's president has made an impassioned plea to Western allies to speed arms deliveries and help stem "terrifying" casualties as Russian forces lay siege to the eastern city of Severodonetsk, destroying the last bridges into the industrial hub.

The cities of Severodonetsk and Lysychansk have been targeted for weeks as the last areas in the eastern Donbas region of Lugansk still under Ukrainian control.

President Volodymyr Zelensky said Monday the human cost of the battle for the region was "simply terrifying". 

Zelensky expressed confidence in Ukraine's ability to reclaim territory, calling on the nation's allies to send more weapons.

"We just need enough weapons to ensure all of this. Our partners have them."

Presidential advisor Mikhaylo Podolyak on Monday listed items he said the Ukrainian army requires, including hundreds of howitzers, tanks and armoured vehicles.

"Being straightforward -- to end the war we need heavy weapons," he tweeted.

- Severodonetsk under siege -

Regional governor Sergiy Gaiday said Monday that Ukraine's forces had been pushed back from Severodonetsk's centre after a weeks-long Russian offensive.

"They destroyed all the bridges, and getting into the city is no longer possible. Evacuation is also not possible," he told Radio Free Europe.

He said Russian forces control 70 to 80 percent of the city but had not captured or encircled it.

Last week, Ukraine's defence minister said up to 100 of his troops were dying daily and 500 sustaining injuries. Previously, Zelensky had estimated 60-100 Ukrainian soldiers were dying daily. 

With the screws tightening on the Lugansk region, Ukrainian forces have two choices: "to surrender or die", said Eduard Basurin, a representative for pro-Russian separatists.

The capture of Severodonetsk would open the road to Sloviansk and another major city, Kramatorsk, in Moscow's push to conquer Donbas, a mainly Russian-speaking region partly held by pro-Kremlin separatists since 2014.

- 'War crimes' -

On Monday, Amnesty International accused Russia of war crimes in Ukraine, saying that attacks on the northeastern city of Kharkiv -- many using banned cluster bombs -- had killed hundreds of civilians. 

"The repeated bombardments of residential neighbourhoods in Kharkiv are indiscriminate attacks which killed and injured hundreds of civilians, and as such constitute war crimes," the rights group said in a report about Ukraine's second-biggest city.

In Bucha, a town near Kyiv that has become synonymous with war crimes allegations, police said they had discovered another seven bodies in a grave.

"Several victims had their hands tied and knees bound," Kyiv regional police chief Andriy Nebytov said on Facebook.

Dozens of bodies in civilian clothing were found in the town in April after Russian troops withdrew from the area following a month-long occupation.

- 'They bomb and they bomb' -

Elsewhere in northern Ukraine on Monday, Russian rocket strikes hit the town of Pryluky, authorities said.

Pryluky, which lies about 150 kilometres (93 miles) east of the capital, is home to a military airfield.

In Donetsk, separatist authorities said three people were killed and four wounded in Ukrainian shelling on a market.

The nearby city of Lysychansk has been massively damaged after months of shelling, with no water, electricity or phone signal.

Ukrainian artillery uses the city's high ground to exchange fire with Russian forces fighting for control of Severodonetsk, just across the river.

Lysychansk resident Maksym Katerin buried his mother and stepfather in his garden Monday after a shell ripped through his yard, killing them instantly.  

"I don't know who did this, but if I knew, I would tear off their arms," said Katerin.

Katerin's neighbour Yevgeniya Panicheva wept, saying Katerin's mother "was lying here, her stomach was ripped and her guts were falling out. She was a very good, kind and helpful woman. Why did they do this to her?"

"They bomb and they bomb and we don't know what to do."

A six-year-old boy was also killed in the city on Sunday, police told AFP.

- Harvest delayed -

Far from the battlefield, World Trade Organization members gathered in Geneva to address the threat to global food security since Russia's invasion.

Ukraine's deputy agriculture minister said on Monday that a quarter of his country's arable land had been lost but insisted national food security was not threatened.

On a farm near the southern Ukrainian city Mykolaiv, the harvest has been delayed by the need to undo damage by Russian troops who passed through the area in March.

"We planted really late because we needed to clear everything beforehand," including bombshells, Nadiia Ivanova, 42, told AFP.

The farm's warehouses currently hold 2,000 tonnes of last season's grain but there are no takers.