KYIV, July 31 (Reuters) - A senior Ukrainian official reported heavy fighting in the northeast of the country on Sunday, with Kyiv's forces holding their lines and making gains in some areas.

Russia's military said it had halted Ukrainian forces in the northeast. The military also said it brought down down three Ukrainian drones which had tried to strike Moscow and damaged a high-rise building reported to house government offices.

Ukrainian President Volodymyr Zelenskiy described Sunday as "a good day, a powerful day" at the front, particularly near Bakhmut, where Ukrainian forces say they are retaking ground lost when Russian forces took the city in May.

Ukraine did not directly claim responsibility for the drone attacks but Zelenskiy said the war was "gradually returning to Russia's territory - to its symbolic centres".

Russian forces launched the latest in a series of night-time air attacks, striking what officials said was a "non-residential building" in the northeastern city of Kharkiv. The hit started a fire but there were no reports of casualties.

Zelenskiy reported that the death toll in a Russian strike on a school in the northern town of Sumy on Saturday had risen to two after rescue teams cleared rubble from the site.

Ukrainian Deputy Defence Minister Hanna Maliar said Russian forces were "trying to drive us out" of elevated positions in the northeast occupied by Moscow after its February 2022 invasion, but retaken later by Ukrainian troops.

The Russians' key task, she told national television, was to "divert our forces from the Bakhmut area, where we have a successful offensive".

"They have attacked endlessly this week. But our troops resist the attacks and sometimes push them back with heavy losses," she said.

Maliar said the Russians had suffered "no fewer losses than during the heated battles in Bakhmut", which fell to Russian forces after more than 10 months of fighting.

Ukraine last month launched a counter offensive focusing on a southward campaign to drive a wedge between Russian forces holding territory in the east and the annexed Crimean peninsula, and on winning back ground around Bakhmut.

But fierce fighting has also flared around the Ukrainian -held northeastern towns of Kupiansk and Lyman.

Maliar said Russian forces were also "tenaciously trying to seize back" areas on the southern front taken by Ukraine.

Ukraine, she said, had recaptured 200 sq. km. (77 sq. miles) in the south, but advances were limited by entrenched Russian positions and mines.

Russia's Defence Ministry, in its daily account of military activity, said its forces had spotted and deployed rockets to destroy an аrmoured brigade of Ukrainian troops near Svatove, a key Russian-held town in the northeast.

Russian forces, it said, had also repelled four Ukrainian attacks near the town of Lyman, further south.

The battlefield accounts could not be independently verified.