Russian forces suffered heavy losses in a Ukrainian attack that destroyed a pontoon bridge they were using to try to cross a river in the east, Ukrainian and British officials said in another sign of Moscow's struggle to salvage a war gone awry.

A ruined pontoon crossing with dozens of destroyed or damaged Russian armored vehicles on both banks of Siverskyi Donets River after their pontoon bridges were blown up in eastern Ukraine. (Source: Associated Press)

Ukrainian authorities, meanwhile, opened the first war crimes trial of the conflict on Friday. The defendant, a captured Russian soldier, stands accused of shooting to death a 62-year-old civilian in the early days of the war.

The trial got underway as Russia’s offensive in the Donbas, Ukraine’s eastern industrial heartland, seemed to turn increasingly into a grinding war of attrition.

Ukraine’s airborne command released photos and video of what it said was a damaged Russian pontoon bridge over the Siversky Donets River and several destroyed or damaged Russian military vehicles nearby. The command said its troops “drowned the Russian occupiers”.

Britain’s Defence Ministry said that Russia lost “significant armoured manoeuvre elements" of at least one battalion tactical group in the attack earlier this week.

“Conducting river crossings in a contested environment is a highly risky manoeuvre and speaks to the pressure the Russian commanders are under to make progress in their operations in eastern Ukraine,” the ministry said in its daily intelligence update.

With Ukraine pleading for more arms to fend off the invasion, the European Union’s foreign affairs chief announced plans to give Kyiv an additional 500 million euros (NZ$831 million) to buy heavy weapons.

Ukrainian Defence Minister Oleksii Reznikov said heavy weapons from the West now making their way to the front lines — including American 155 mm howitzers — will take some time to turn the tide in Ukraine's favour. He admitted there is no quick end to the war in sight.

“We are entering a new, long-term phase of the war,” Reznikov wrote in a Facebook post. “Extremely difficult weeks await us. How many there will be? No one can say for sure.”

The battle for the Donbas has turned into a village-by-village, back-and-forth slog with no major breakthroughs on either side and little ground gained.

Fierce fighting has been taking place on the Siversky Donets River near the city of Severodonetsk, said Oleh Zhdanov, an independent Ukrainian military analyst. The Ukrainian military has launched counterattacks but has failed to halt Russia's advance, he said.

"The fate of a large portion of the Ukrainian army is being decided — there are about 40,000 Ukrainian soldiers,” he said.

A ruined pontoon crossing with dozens of destroyed or damaged Russian armoured vehicles on both banks of Siverskyi Donets River. (Source: Associated Press)

The Ukrainian military chief for the Luhansk region of the Donbas said Friday that Russian forces opened fire 31 times on residential areas the day before, destroying dozens of homes, notably in Hirske and Popasnianska villages, and a bridge in Rubizhne.

In the south, Ukrainian officials claimed another success in the Black Sea, saying their forces took out another Russian ship, though there was no confirmation from Russia and no casualties were reported.

The Vsevolod Bobrov logistics ship was badly damaged but not thought to have sunk when it was struck while trying to deliver an anti-aircraft system to Snake Island, said Oleksiy Arestovych, a Ukrainian presidential adviser.

In April, Ukraine sank the Moskva, a guided missile cruiser that was the flagship of Russia’s Black Sea fleet. In March it destroyed a landing ship.

Justin Crump, a former British tank commander who is now a security consultant, said Moscow's losses have forced it to downsize its objectives. He said the Russians have had to use hastily patched-together units that haven't trained together and are thus less effective.

“This is not going to be quick. So we’re settled in for a summer of fighting at least. I think the Russian side is very clear that this is going to take a long time,” he said.

Ukrainian prosecutors are investigating thousands of potential war crimes. Many of the alleged atrocities came to light last month after Moscow’s forces abandoned their bid to capture Kyiv and withdrew from around the capital, exposing mass graves and streets strewn with bodies.

In the first war crime case brought to trial, Russian Sergeant Vadim Shyshimarin, 21, could get life in prison if convicted of shooting a Ukrainian man in the head through an open car window in a village in the northeastern Sumy region on February 28, four days into the invasion.

In a small Kyiv courtroom, scores of journalists watched the start of the wartime proceedings, which will be closely watched by international observers to make sure the trial is fair.

The defendant, dressed in a blue and grey hoodie and grey sweatpants, sat in a small glass cage during the proceedings, which lasted about 15 minutes and will resume on Wednesday.

Shyshimarin was asked a series of questions, including whether he understood his rights and whether he wanted a jury trial. He declined the latter.

His Ukraine-assigned attorney, Victor Ovsyanikov, has acknowledged that the case against the soldier is strong and has not indicated what his defence will be.

Shyshimarin, a member of a tank unit that was captured by Ukrainian forces, admitted that he shot the civilian in a video posted by the Security Service of Ukraine, saying he was ordered to do so.

Russian army Sergeant Vadim Shishimarin, 21, is seen behind a glass during a court hearing in Kyiv, Ukraine. (Source: Associated Press)

As the war grinds on, teachers are trying to restore some sense of normalcy after the fighting shuttered Ukraine’s schools and upended the lives of millions of children.

In Kharkiv, Ukraine’s second-largest city, lessons are being given in a subway station that has become home for many families. Children joined their teacher Valeriy Leiko around a table to learn about history art, with youngsters’ drawings lining the walls.

“It helps to support them mentally. Because now there is a war, and many lost their homes ... some people’s parents are fighting now,” Leiko said. In part because of the lessons, he said, “they feel that someone loves them.”

An older student, Anna Fedoryaka, monitored a professor's online lectures on Ukrainian literature.

The internet connection was a problem for some, she said. And “it is hard to concentrate when you have to do your homework with explosions by your window."