Zelensky urges Russians to 'go home' as Ukraine presses offensive in south

Ukrainian President Volodymyr Zelensky has urged Russian troops to flee from an offensive launched by his forces near the southern city of Kherson saying Ukraine's military were taking back their territory, though Russia said the assault had failed.

Ukraine's assault comes after weeks of a stalemate in a war that has killed thousands, displaced millions, destroyed cities and caused a global energy and food crisis amid unprecedented economic sanctions.

It has also fuelled worries of a radiation disaster being triggered by shelling near the south Ukraine Zaporizhzhia nuclear plant.

Zelensky, in his nightly address late on Monday, vowed that Ukrainian troops would chase the Russian army "to the border".

"If they want to survive - it's time for the Russian military to run away. Go home," he said.

"Ukraine is taking back its own," Zelensky said.

Oleksiy Arestovych, a senior adviser to Zelensky, said Russian defences had been "broken through in a few hours".

Ukrainian forces were shelling ferries that Russia was using to supply a pocket of territory on the west bank of the Dnipro river in the Kherson region, he added.

Russia's defence ministry said Ukrainian troops had attempted an offensive in the Mykolaiv and Kherson regions but sustained significant casualties, RIA news agency reported.

The "enemy's offensive attempt failed miserably", it said.

But a Ukrainian barrage of rockets left the Russian-occupied town of Nova Kakhovka without water or power, officials at the Russian-appointed authority told RIA news agency.

Reuters could not verify the battlefield reports.

Russian shelling of the port city of Mykolaiv, which has remained in Ukrainian hands despite repeated Russian bombardments, killed at least two people, wounded some 24 and wiped out homes, city officials and witnesses said on Monday.

A Reuters correspondent reported a strike hit a family home directly next to a school, killing one woman. 

The owner of the property, Olexandr Shulga, said he had lived there his entire life and that his wife died when she was buried in debris. "It hit and the shockwave came. It destroyed everything," he said.

Russia invaded Ukraine on Feb 24 to wage what it says is a "special military operation" to rid Ukraine of nationalists and protect Russian-speaking communities. Ukraine and its allies describe it as an unprovoked war of aggression.

The conflict, the biggest attack on a European state since 1945, has largely settled into a war of attrition, mainly in the south and east, marked by artillery bombardments and air strikes. Russia captured swathes of the south early on.

Ukraine's southern command said its troops had launched offensive actions in several directions, including in the Kherson region north of the Crimean peninsula that Russia annexed from Ukraine in 2014.

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 offensive, saying Russian forces in the south remained "quite powerful".

IAEA nuclear mission

The Zaporizhzhia nuclear power plant in Ukraine's south, captured by Russian troops in March but still manned by Ukrainian staff, has been a hotspot in the conflict with both sides trading blame for shelling in the vicinity.

A mission from the International Atomic Energy Agency (IAEA) is headed to the facility, Europe's largest nuclear plant, and is due later this week to inspect and assess any damage.

Led by IAEA chief Rafael Grossi, the mission will 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.

A top Russian diplomat said Moscow hoped the mission would dispel misconceptions about the plant's allegedly poor state. 

The Kremlin said the IAEA mission was "necessary" and urged the international community to pressure Ukraine to reduce military tensions at the plant. The mission must do its work in a politically neutral manner, Russia's foreign ministry said.

The United Nations, US and Ukraine have called for the withdrawal of military equipment and personnel from the complex to ensure it is not a target. 

"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," White House National Security Council spokesperson John Kirby said.

But the Kremlin again ruled out vacating the site.