(Adds some IAEA members seen leaving, return to school)
* Team was delayed several hours by shelling near plant
* Each side accuses other of trying to sabotage IAEA mission
* Shelling reported at Enerhodar, site of plant, overnight
* Ukraine claims successes in counter-offensive
By Tom Balmforth
ZAPORIZHZHIA, Ukraine, Sept 1 (Reuters) - A team of U.N. experts arrived at Europe's biggest atomic power plant after crossing the frontline into Russian-held territory in southern Ukraine on Thursday, to assess the risk of what both sides say could be a devastating radiation disaster.
After being delayed several hours by shelling near the site, the team reached the Zaporizhzhia nuclear power plant in a large convoy with a heavy presence of Russian soldiers nearby.
A Reuters reporting crew operating in Russian-held territory was at the site. Some members of the inspection team left after spending several hours there. Ukraine's nuclear power operator Energoatom said five team members would stay on for two more days.
Russia and Ukraine have accused each other of trying to sabotage the IAEA mission to the plant, which sits on the south bank of a huge reservoir on the Dnipro River that divides Russian and Ukrainian forces in central southern Ukraine. Since the early days of the conflict, the plant has been controlled by Russian troops but operated by Ukrainian staff.
Conditions at the plant have been unravelling for weeks, with Moscow and Kyiv regularly trading blame for shelling in the vicinity, fuelling fears of a Chornobyl-style radiation disaster.
Kyiv also accuses Moscow of using the Russian-controlled plant as a shield for its weapons, which Russia denies, and of planning to switch it from Ukraine's power grid to Russia's, effectively stealing its output.
Russia's Foreign Minister Sergei Lavrov said Moscow was doing everything to ensure that the plant could operate safely, and for the IAEA inspectors to be able to complete their tasks.
"In the event of further attempts by Kyiv to disrupt their work with shelling or sabotage, the entire responsibility for the consequences will fall entirely on the Zelenskiy regime and its handlers and their 'support group' in the West," the Russian foreign ministry said in a statement, referring to Ukraine's President Volodymyr Zelenskiy.
Earlier, Ukraine's state nuclear company Energoatom said Russian shelling had forced the shutdown of one of the two reactors still operating at the site, while Moscow said it had thwarted a Ukrainian attempt to seize the plant.
A Reuters reporter in the nearby Russian-controlled town of Enerhodar said a residential building was struck by shelling, forcing people to take cover in a basement. It was not possible to establish who had fired.
The Russian-installed governor of Zaporizhzhia district, Yevgeny Balitsky, said at least three people had been killed and five wounded in what he called Ukrainian shelling of Enerhodar that destroyed three kindergartens and a culture centre.
Kyiv said the incident was staged by the Russians to blame Ukraine.
Russia captured much of Zaporizhzhia region in the first weeks of its Feb. 24 invasion, but the province's biggest city, Zaporizhzhia, still rests in Ukrainian hands at the mouth of the reservoir.
The nuclear plant supplied more than a fifth of Ukraine's electricity before the war, and is a vital asset for Ukraine as it braces for a brutal winter of energy shortages.
In recent days, Ukraine has launched a major counter-offensive to recapture territory in southern Ukraine, mainly further down the Dnipro in neighbouring Kherson province.
'PROVOCATION'
IAEA chief Rafael Grossi told reporters early on Thursday in Zaporizhzhia, 55 km (34 miles) from the plant, that he was aware of "increased military activity in the area" but would press ahead with the plan to visit the facility and meet staff.
Moscow accused Ukrainian forces of trying to seize the plant hours before the IAEA team was due to arrive.
Russia's defence ministry said up to 60 Ukrainian troops had crossed the Dnipro in boats at 6:00 a.m. local time (0300 GMT), in what it said was a "provocation" aimed at disrupting the IAEA visit.
It said "measures had been taken" to destroy the opposing troops, including use of military aviation. A local Russian-installed official, Vladimir Rogov, later said "around 40" of the 60 Ukrainian troops had been killed. Russian troops also captured three Ukrainian servicemen during the assault on the plant, he added. Reuters could not verify those reports.
Ukrainian officials have welcomed the IAEA visit, expressing hope that it will lead to the demilitarisation of the plant.
Reuters journalists who accompanied the IAEA mission as far as Zaporizhzhia saw flashes of explosions in the night sky.
Russian-installed officials have suggested that the team from the U.N. nuclear watchdog would have only a day to inspect the plant, while the mission had prepared for longer.
"If we are able to establish a permanent presence, or a continued presence, then it's going to be prolonged. But this first segment is going to take a few days," Grossi had said.
'SLOW PROCESS'
Both sides have claimed battlefield successes in the new Ukrainian push to recapture territory in the south, although details have been scarce so far, with Ukrainian officials releasing little information about their advance.
"It is a very slow process, because we value people," said Oleksiy Arestovych, an adviser to Zelenskiy, referring to the Ukrainian offensive. Moscow has denied reports of Ukrainian progress and said its troops had routed Ukrainian forces.
Millions of people have fled Ukraine, thousands have been killed and cities have been reduced to rubble in what Kyiv and the West call Russia's unprovoked war of agression. Moscow calls its actions a "special military operation" to rid Ukraine of nationalists and protect Russian-speaking communities.
Schoolchildren returned to desks in some areas for the start of the Ukrainian school year. Ukrainian children who fled the country also started new schools across central Europe for the first time on Thursday.
But in Mykolaiv near the frontline in southern Ukraine, children went to their bombed-out school only to take their books home. Most schools in the area will stay shut.
"My heart is broken because I love this school," said Viktoria Poliakova, deputy head teacher, as she looked at the damage.
(Reporting by Tom Balmforth in Zaporizhzhia, Ukraine, and by Reuters bureaus; Writing by Gareth Jones, Alexandra Hudson; Editing by Philippa Fletcher and Peter Graff)