By Serhiy Chalyi

ZAPORIZHZHIA, Ukraine (Reuters) -Russian attacks overnight and on Wednesday killed at least 10 civilians in Ukraine, while senior Ukrainian military officials said their troops had made some headway in counteroffensive operations in the southern theatre.

President Volodymyr Zelenskiy, in his nightly video address, said the death toll had risen to five from four in a morning missile strike on a residential building in the southeastern city of Zaporizhzhia.

Officials said a 31-year-old woman was killed in an attack on the village of Obukhivka in the central region of Dnipropetrovsk and a man and a woman were killed in an overnight attack on the southern region of Kherson.

On Wednesday evening, Ukraine's Interior Ministry said two bodies had been pulled out from under the rubble of a food shop hit by a Russian missile near the southern city of Mykolaiv.

Local officials in Sumy region, on the Russian border, said an "infrastructure site" had been hit in a drone attack, but provided no further details.

"The evil state continues to use terror and wage war on civilians. Russian terror must be defeated," Zelenskiy wrote on the Telegram messaging app.

The apartment building in Zaporizhzhia suffered serious damage to one entrance from the third to the fifth storeys, he said. A picture posted by Zelenskiy on Telegram showed the building with a gaping hole in the middle, its entrance destroyed and windows smashed.

In Obukhivka, near the city of Dnipro, residents said a strong explosion blew out windows and knocked people to the ground. Officials said about 20 houses were damaged.

"A woman all covered in blood ran out from one of the houses, shouting and crying. I think that her daughter died," Victor, 32, a construction worker, told Reuters television. "We entered the house and saw a dead girl."

SOUTHERN ADVANCE CONTINUES: GENERAL

General Oleksandr Tarnavskyi, in charge of Ukraine's operations in the south, said Ukrainian forces were proceeding with their planned advance towards the Sea of Azov.

Troops from the Tavria, or southern, group of forces "are continuing their offensive. They have had partial success to the south of Robotyne," Tarnavskyi wrote on Telegram.

Robotyne is one of a group of villages in the south that Ukraine wants to secure as part of the advance - aimed at severing a land bridge linking Russian positions in the south and east.

Oleksandr Shtupun, a spokesperson for southern troops, also reported progress near Robotyne.

Shtupun told national television that shelling had eased around the town of Avdiivka, the focus of fierce Russian attacks in the past week west of the Russian-held town of Donetsk. But troops in the sector were preparing for a variety of scenarios.

Ukrainian troops are also trying to recapture land in eastern regions.

The General Staff, in its evening report, said its forces had repelled attacks in several areas of the 1,000-km (620-mile) front line - including 15 around the long-contested town of Maryinka in Donetsk region and 10 further north near Kupiansk.

Russia's Defence Ministry gave few details of its troops' operations, but said a depot of Ukrainian aviation equipment had been destroyed in central Dnipropetrovsk region.

Reuters could not verify accounts from either side.

(Additional reporting by Olena Harmash and Pavel Polityuk in Kyiv, and Lidia Kelly in Melbourne; Editing by Timothy Heritage, Ron Popeski, Grant McCool and Diane Craft)