Ukrainian sources have indicated that thousands of troops have been committed to its incursion into Russia’s Kursk province, as dramatic pictures emerged of a fire at the occupied Zaporizhzhia nuclear power plant 250 miles to the south.

A Ukrainian security official told the Agence France-Presse that the aim of the incursion was to destabilise Russia and string out Russian forces with light, fast-moving attacks. It remains unclear how sustainable the operation will be in the medium term amid Kremlin threats that it will be snuffed out using Russian reserves.

Russia had suggested that several hundred Ukrainian troops had launched a surprise attack on Tuesday, but the Ukrainian official said the numbers were larger. Asked whether more than 1,000 Ukrainian soldiers were involved, the official said: “It is a lot more … Thousands.”

Several Ukrainian brigades are said to be involved in the operation, according to a range of sources. Kyiv caught Russia off guard by striking at a lightly defended sector of the front that had seen no significant fighting since the spring of 2022 – and broke through limited border defences.

“We are on the offensive. The aim is to stretch the positions of the enemy, to inflict maximum losses and to destabilise the situation in Russia as they are unable to protect their own border,” the security official said on condition of anonymity.

Later on Sunday, Ukraine’s president, Volodymyr Zelenskiy, highlighted that Russian forces appeared to have started a fire in one of the cooling towers of the Zaporizhzhia nuclear power plant that it has occupied since the early days of the war.

“Radiation levels are within norm,” Zelenskiy said before accusing Russia of using its control of the site, whose six reactors are in shutdown mode, “to blackmail Ukraine, all of Europe, and the world”.

A Ukrainian official in Nikopol, the nearest town across the river Dnipro from the nuclear plant, added that according to “unofficial information”, the fire was caused by setting fire to “a large number of automobile tyres” in a cooling tower.

Video and pictures showed smoke dramatically billowing from one of the towers, although experts said they are not in use while the reactor is in shutdown mode, prompting some to question whether it was a way of trying raise the stakes over Ukraine’s incursion into Russia.

Late on Sunday night, the state-run Tass news agency cited Russia’s state nuclear energy company, Rosatom, as saying that the main fire had been extinguished, while Russian and Ukrainian authorities said one of the cooling towers appeared to have been damaged.

There has been speculation that Ukraine may try to capture a Russian nuclear power plant at Kurchatov near Kursk, but it is more than 30 miles from the current fighting and it is thought that it would be a stretch for Kyiv’s forces to reach that far.

Ukraine’s leaders and its military have said little about the purpose of the incursion. It is generally believed to be intended to ease pressure on the eastern Donbas front where Russian forces have been grinding out advances. It is also seen as demonstrating to Russia and Ukraine’s western backers that Kyiv is still capable of attacking successfully.

Russia’s defence ministry said it had thwarted attacks by Ukrainian “mobile groups” in three villages north and east of Korenevo – Tolpino, Zhuravli, Obshchiy Kolodez – all 15 to 18 miles from the border, the farthest points at which Moscow has acknowledged the incursion to have reached.

A pro-Ukrainian Telegram channel released a video of soldiers raising a flag over a building in the Russian village of Guevo, a couple of miles inside the border and seven miles south of Sudzha, one of the first towns reached during the incursion.

On Saturday, Ukraine’s president, Volodymyr Zelenskiy, finally directly acknowledged the incursion into Kursk oblast – the first time Kyiv’s regular forces have attacked inside Russia since the Kremlin launched its full-scale invasion in February 2022.

“Today, I received several reports from Commander-in-chief [Oleskandr] Syrskyi regarding the frontlines and our actions to push the war on to the aggressor’s territory,” he said late on Saturday. “Ukraine is proving that it can indeed restore justice and is ensuring the exact kind of pressure that is needed – pressure on the aggressor.”

Maria Zakharova, Russia’s foreign ministry spokesperson, accused Kyiv of being engaged in “terrorist activity” aimed at striking fear in ordinary Russians. “It understands perfectly well that these barbaric acts make no sense from a military point of view, but it continues to work off the loans issued by its masters,” she added.

Fifteen people were injured in Kursk, the acting regional governor, Alexei Smirnov, said, after debris from a missile hit an apartment building. Zakharova said Ukrainian forces had launched a “massive missile strike” on the city and that one had got through, causing casualties.

Russia’s military appears to be relying on defending Kursk with a mixture of conscript border guards, elements from other regional forces and those “redeployed from lower-priority frontline areas in Ukraine”, according to an overnight analysis from the Institute for the Study of War (ISW) thinktank, which added that it was likely to exacerbate “the disorganisation of Russia’s chosen response”.

The ISW said the leadership of the effort to end the Ukrainian incursion had probably passed to Russia’s FSB internal security agency after the Kremlin announced on Friday that the response was a “counter-terrorism operation”. Russian federal law subordinates the military to the head of the counter-terrorism operation, the thinktank said.

Meanwhile, an overnight missile attack near Kyiv killed a man and his four-year-old son, emergency services said. Explosions rang out on Saturday night in the centre and east of Kyiv after Ukraine’s air force said two Russian missiles were heading towards the city.