Ukrainian President Volodymyr Zelenskiy told Russian soldiers holding the southern city of Kherson to “run for your lives” as Ukraine finally launched a much-anticipated counterattack to retake the first city to fall following the invasion in February.

Ukraine said on August 30 that it had launched an offensive in the southern theatre after talking about a counteroffensive for almost two months.

Local residents in Kherson reported on social media they heard explosions and shots for a second day on August 30, but did not know who was responsible or where exactly the fighting was. Blasts had earlier been reported in Nova Kakhovka, some 55 km north-east, and Russia's state-run Ria Novosti news agency reported the city was left without electricity and water supply overnight.

Oleksiy Arestovych, a senior Ukrainian presidential adviser, said Russian defences in the Kherson region had been "broken through in a few hours," but didn’t make it clear if the forces had broken through Russia’s fortified defences of the city or if he was referring to skirmishes on the outskirts.

In an update early today, a spokesman for Ukraine's southern operational command said 13 Russian command posts had been destroyed, as well as three ammunition depots and a crossing over the Dnipro river, the BBC reports.

Other reports claimed that Ukraine forces had captured four more villages close to Kherson but had not entered the city. On Russian social media some were reporting they had talked friends in the city and that there were no Ukrainian soldiers inside the city as of the middle of day on August 30.

But fierce fighting has been reported on the outskirts of the city. Information is scarce after the Ministry of Defence appealed to the population not to share information, videos or pictures of the fighting that could be used to tactical advantage by Russia.

Kherson fell shortly after the war began without a shot fired, given up to the invading troops by its local governor. It is the only city that Russia holds on the western bank of the Dnipro river and could serve as a base for Russian military operations further west.

The city is strategically important as it also controls the water that flows into Crimea. For much of the last eight years Kyiv has blocked off the canals that feed into Crimea, causing a severe water shortage and leading the Kremlin to consider building a very expensive desalination plant to supply the peninsula with fresh water and irrigation.

While details are sketchy, the Ukrainian forces appear to be trying to cut the troops in the city off from the three bridges that connect Kherson to the eastern bank of the Dnieper that are under Russian control, and make it impossible to resupply the defenders.

Arestovych also said Ukrainian forces were shelling ferries Russia has been using to supply the city in an enclave of land on the west bank of the Dnipro river and east of Kherson itself.

Kyiv has been talking about a major offensive against Kherson for well over a month, but the lack of supplies and munitions meant that it has been delayed. In the meantime, Russia has brought up reinforcements to the city from Donbas, but in doing so has depleted its forces there, where fighting has ground to a stalemate. Russia has a reported 25-30 battalion tactical groups (BTG) in Kherson, but Kyiv has successfully bombed the three bridges leading to the city, making them impassable. At the same time, Russia has set up a pontoon bridge, but that too has been targeted by the Ukrainian forces. Altogether there are an estimated 20,000 Russian troops stationed in Kherson who have no other means of supply than the bridges across the river.

In his regular video address on August 30, Zelenskiy called on Russian forces to go home or be chased home.

"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 (land)," he added but refrained from giving any operational details or results.

British intelligence sources told the press that Kyiv had launched an artillery barrage along the entire southern front, but said it could not report any Ukrainian territorial advances at this time.

Russia's RIA news agency reported that the Russian-controlled town of Nova Kakhovka had been left without water or power after a Ukrainian missile strike, Russia's defence ministry said the Ukrainian offensive had been halted in its tracks.

The Russian ministry said in a statement that Ukrainian forces had launched a trio of attacks in both the Kherson and Mykolaiv regions, but had already lost some 560 troops, 26 tanks and two warplanes, reports Reuters.

Russian shelling of Mykolaiv killed at least two people, injured some 24 others and wiped out homes, according to city officials and witnesses, reports Reuters.

The strike hit a family home directly next to a school on August 29, killing one woman, according to a Reuters correspondent at the scene. Both houses on the property were left in ruins, with large craters gouged out of the ground in front.

A Russian official in Kherson told Russian media that forces had discovered a Ukrainian sabotage team inside the city and destroyed it.

The recapture of Kherson would be a major propaganda coup for Zelenskiy, as the Ukrainian forces have yet to liberate any of the larger towns occupied by Russian forces. In July Russia took control of all of the Luhansk region and controls more than half of the Donetsk region, although progress has ground to a halt more recently and Russia has not made any more gains in recent weeks, according to the Kyiv military authorities.

In an effort to bolster his forces, Putin signed a decree on August 29 to expand the military to 2mn men. The decree increases the armed forces by 137,000 personnel, Russian state news agency Ria Novosti reported. The armed forces will employ up to 1.15mn military personnel and 890,000 non-military personnel, according to the decree.

Bankova, the presidential seat in Kyiv, has hardened its line since several rounds of potential peace talks came to nothing in July.

Zelenskiy has taken a much harder line, saying that he will accept nothing short of the total expulsion of Russian forces from Ukraine, including the return of both the Donbas region and the Crimea peninsula.

"Russia has turned our peninsula, which has always been and will be one of the best places in Europe, into one of the most dangerous places in Europe. Russia brought large-scale repression, environmental problems, economic hopelessness and war to Crimea." Zelenskiy said in a recent video broadcast that "it is impossible to say" when the liberation will happen, but Ukraine is constantly "adding the necessary components to the formula of liberation of Crimea."