Russian troops have entered the outskirts of the Ukrainian city of Sievierodonetsk, according to the regional governor, who described fierce fighting on Monday over the ruins of a city that has become the focus of Moscow’s offensive.

Russia has concentrated its firepower on the last major population centre still held by Ukrainian forces in the eastern Luhansk province, in a push to achieve one of President Vladimir Putin’s stated objectives after three months of war.

Incessant shelling has left Ukrainian forces defending ruins in Sievierodonetsk, but their refusal to withdraw has slowed the wider Russian offensive across the Donbas region. Luhansk region governor Serhiy Gaidai said Russian troops had advanced into the city’s southeastern and northeastern fringes.

The Russians “use the same tactics over and over again. They shell for several hours — for three, four, five hours — in a row and then attack”, Gaidai said.

“Those who attack die. Then shelling and attack follow again, and so on until they break through somewhere.”

With temperatures rising, he said there was a “terrible smell of death” on the outskirts of the city. But he said Ukrainian forces had driven the Russians out of the village of Toshkivka to the south, potentially frustrating Moscow’s push to encircle the area.

Gaidai later said a French journalist had been killed by shrapnel that pierced his vehicle, and that evacuations from the area had been halted.

In a speech, Ukrainian President Volodymyr Zelensky described capturing Sievierodonetsk as “a fundamental task for the occupiers”.

“Some 90% of buildings are damaged. More than two-thirds of the city’s housing stock has been completely destroyed,” he said. Ukraine’s defence ministry said Moscow was also trying to regroup to attack the strategically important town of Sloviansk, further west.

Capturing Sievierodonetsk and its twin city Lysychansk on the opposite bank of the Siverskyi Donets river would give Russia effective control of Luhansk province, a point at which the Kremlin might be able to declare some form of victory.

But by focusing its effort on a battle for the single small city — Sievierodonetsk housed only around 100,000 people before the war — Russia might be leaving other territory open to eventual Ukrainian counterstrikes.

The past few days have seen initial signs of a potential Ukrainian counteroffensive in the south, where Moscow is trying to consolidate its control of Kherson province.

Kyiv says its forces pushed back Russian troops in recent days to defensive positions in three villages — Andriyivka, Lozove and Bilohorka — all located on the south bank of the Inhulets river that forms the border of Kherson.

The Institute for the Study of War think tank said this counterattack so far did not appear likely to retake substantial territory in the near term, but could disrupt Russian operations and force Moscow to reinforce the area.

French foreign minister Catherine Colonna became the latest western dignitary to go to Kyiv, visiting a mass grave in the suburb of Bucha.