By Andrea Shalal and Max Hunder
MYKOLAIV, Ukraine/KYIV (Reuters) - Ukrainian troops bolstered by stepped-up Western military aid launched a long-awaited counter-offensive to retake territory in the south on Monday as Russian forces shelled residential areas of the Black Sea port city of Mykolaiv.
Moscow acknowledged a new offensive had been launched but said it had failed and the Ukrainians had suffered significant casualties.
But a Ukrainian barrage of rockets left the Russian-occupied town of Nova Kakhovka without water or power, officials at the Russian-appointed local authority told RIA news agency.
Ukraine's new military attack came after several weeks of relative stalemate in a war that has killed thousands, displaced millions, destroyed cities and caused a global energy and food crisis amid unprecedented economic sanctions.
Russian shelling of Mykolaiv killed at least two people, injured some 24 others and wiped out homes, according to city officials and witnesses.
The conflict, the biggest attack on a European state since 1945, had largely settled into a war of attrition, mainly in the south and east, marked by artillery bombardments and air strikes.
Russia captured swathes of Ukraine's south near the Black Sea coast in its early phase.
Ukraine's southern command said its troops had started offensive actions in several directions in the south, including in the Kherson region which lies north of the Russian-annexed Crimean peninsula.
Ukraine had struck more than 10 sites in the past week and "unquestionably weakened the enemy", according to a spokeswoman who declined to give details of the counter-offensive, saying Russian forces in the south remained "quite powerful".
Ukraine has been using sophisticated Western-supplied weapons to hit Russian ammunition dumps and wreak havoc with supply lines.
Russia's defence ministry said Ukrainian troops had attempted an offensive in the southern Mykolaiv and Kherson regions but sustained significant casualties, RIA news agency reported
"(The) enemy's offensive attempt failed miserably," it said.
Reuters could not independently verify the battlefield reports.
In Mykolaiv, where Russian shelling hit residential areas, a Reuters correspondent said a strike hit a family home directly next to a school, killing one woman.
The owner of the property, Olexandr Shulga, told Reuters he had lived there his entire life and that his wife - who was in a different room when the missile struck - died when she was buried in debris.
"It hit and the shockwave came. It destroyed everything," he said.
A shipbuilding centre and port on the Southern Bug river just off the Black Sea, Mykolaiv has suffered heavy Russian bombardments throughout the war but remained in Ukrainian hands.
Russia says it is waging a "special military operation" in Ukraine to rid it of nationalists and protect Russian-speaking communities. Ukraine and the West describe Russia's actions as an unprovoked war of aggression.
The world is also scrambling to avoid a disaster at the Russian-occupied Zaporizhzhia nuclear plant, Europe's largest nuclear plant, where both sides have traded accusations of shelling in its vicinity.
A mission from the International Atomic Energy Agency (IAEA) to the facility, captured by Russian forces in March but still run by Ukrainian staff, was due to arrive in Kyiv on Monday and start work in the coming days, Ukraine said.
Led by IAEA chief Rafael Grossi, the mission will assess physical damage, evaluate working conditions and check safety and security systems, the Vienna-based organisation said.
It will also "perform urgent safeguards activities", a reference to keeping track of nuclear material.
On Monday, Russian-installed officials said a Ukrainian missile strike had punched a hole in the roof of a fuel depot at the plant.
Russia's defence ministry said its forces had shot down a Ukrainian drone that was trying to attack the complex, Russian news agencies reported. It said there was no serious damage and radiation levels were normal.
Reuters could not independently verify either report.
The Kremlin said the IAEA mission was "necessary" and urged the international community to pressure Ukraine to reduce military tensions at the plant. The IAEA mission must carry out its work in a politically neutral manner, Russia's foreign ministry said.
The United Nations, United States and Ukraine have called for the demilitarization of the complex.
"We continue to believe that a controlled shutdown of the Zaporizhzhia nuclear reactors would be the safest and least risky option in the near-term," said White House National Security Council spokesperson John Kirby.
But the Kremlin again ruled out vacating the site.
Liliia Vaulina, 22, one of a number of civilians who had fled Enerhodar for the Ukrainian-held city of Zaporizhzhia, some 50 km (30 miles) upriver from the plant, said she hoped the IAEA mission would lead to a demilitarisation of its area.
"I think that they will stop the bombing," she told Reuters.
(Additional reporting by Pavel Polityuk in Kyiv and Reuters bureaus; Writing by Gareth Jones, Angus MacSwan and Costas Pitas; Editing by Mark Heinrich, Alex Richardson, Nick Macfie and Cynthia Osterman)