Russian missiles slammed into Ukraine’s second-largest city in the northeast of the country and killed at least seven civilians early Thursday, officials said, as Kyiv’s army laboured to hold off an intense cross-border offensive by the Kremlin’s larger and better-equipped forces.

At least 16 people were injured as S-300 missiles struck the city of Kharkiv, regional governor Oleh Syniehubov said. The sound of 15 explosions reverberated around the city of some 1 million people.

Ukrainian President Volodymyr Zelensky called the attack “extremely cruel”. He expressed renewed frustration at not getting enough air defence systems from the country’s western partners to prevent the barrages after more than two years of unrelenting war.

The city of Kharkiv, which is the capital of the region of the same name, lies about 20km from the Russian border. Moscow’s troops have in recent weeks captured villages in the area as part of a broad push, and analysts say they may be trying to get within artillery range of the city.

In what is shaping up to be Ukraine’s biggest test since Russia’s full-scale invasion in February 2022, outnumbered and outgunned Ukrainian forces are being pressed at several points along the about 1,000-km front line that snakes from north to south along the eastern side of the country.

With Ukraine short of air defences and waiting for more western military support that recently started trickling in, its army has been pushed backwards in places while Russia has pounded its power grid and civilian areas. Kyiv endured further power outages on Thursday.

Zelensky said the main hotspots in recent fighting have been Kharkiv and the neighbouring Donetsk region, where in February Ukraine’s defenders withdrew from the stronghold of Avdiivka.

For the Kremlin, taking control of all of the partially occupied Donetsk is a war priority.

At the same time, and in an apparent effort to stretch Ukraine’s depleted forces, Russian troops have made incursions in the northern Sumy region.

Nearly 1,500 people, including 200 children, have been evacuated from the towns of Bilopillia and Vorozhba in that region, according to regional governor Volodymyr Artiukh.

“The main focus (of the fighting) is on the entire border area,” Zelensky said in his nightly video address on Wednesday.

Ukraine has also trained its sights on Russian regions across the border. Russia’s defence ministry said on Thursday that 35 Ukrainian rockets and three drones were shot down over the Belgorod region. Regional governor Vyacheslav Gladkov said one drone struck a house and exploded after being shot down, killing a woman.