Ukraine urged civilians near the northeastern front line to evacuate on Thursday as Russia ramped up an assault to capture territory already once seized during the conflict.

Kupiansk and the surrounding areas of Ukraine's Kharkiv region was recaptured by Kyiv's forces last September, but Moscow has since pushed back on the region.

"Given the difficult security situation and the increasing amount of shelling by Russian terrorist forces in Kupiansk community, you have the opportunity to evacuate to a safer place," the city administration said, naming 37 settlements wedged between the town and Russian lines.

It said residents could evacuate to Kharkiv, some 56 miles (90 kilometres) west, where they would have the option to move to safer regions, urging children, the elderly and the sick to leave.

"Do not neglect your safety and the safety of your loved ones," it said.

The warning came as Russia's defence ministry announced its soldiers had "improved their position" along the front line near the town, after reporting advances earlier in the week.

"In the course of offensive operations near Kupiansk, assault teams of the Western battle group improved their positions along the forward edge of the front line," it said in a daily briefing.

- 'Getting dangerous' -

"It looks like the Russians are erasing places in the Kupiansk area," said Rostyslav Melnykiv, professor at a local university in Kharkiv.

"People are in danger of losing their lives, not just their homes," he told AFP.

One resident in the small town of Kivsharivka just outside of Kupiansk said she was preparing to evacuate with her children, while her husband refused to leave to care for his elderly mother.

"It's hard to leave them behind," Anna Koresh, 36, told AFP by phone.

"But since it's getting dangerous it's important to take the kids to a safe place."

In Russia, the governor of the Bryansk region said Thursday that two people had been killed after Ukraine shelled the small village of Chausy, about 3 miles from the border.

Russian regions bordering Ukraine have repeatedly accused Kyiv's forces of indiscriminate shelling that has damaged infrastructure and caused civilian deaths.

Ukraine launched a highly anticipated counteroffensive in June after stockpiling Western weapons, but it has acknowledged difficult battles as it struggles to make headway.

Moscow said earlier Thursday it downed 11 Ukrainian drones nearing the Crimean peninsula and two headed for Moscow, in the latest wave of attacks targeting Russia and Russian-held territory.

"As a result of the thwarted terrorist attacks, there were no casualties or damage," the Russian defence ministry said in a statement on Telegram.

- Drone attacks -

Moscow was largely spared in the early months of the war but the number of drone attacks on the capital has risen in recent months, with the city targeted multiple times this week.

Two people were killed after Ukraine shelled a small village in the Russian border region of Bryansk that has seen regular shelling and drone strikes, the regional governor said.

Meanwhile in the Russian-occupied territory of Nova Kakhovka one person died and one was wounded in Ukrainian shelling, the Moscow-backed administration said on Telegram.

Ukrainian President Volodymyr Zelensky warned last month that "war" was coming to Russia, and that the country's "symbolic centres and military bases" would become targets.

On the other side of the front line, an oil depot in Ukraine's Rivne region was destroyed during a "massive drone attack" on Thursday, governor Vitaliy Koval said, adding that emergency services and investigators were on the scene.

Tensions have also risen on the Black Sea since Russia exited a grain deal agreement allowing safe passage for grain exports from the transit hubs.

In a challenge to Russia, which announced in July that it would consider any ship nearing Ukraine in the Black Sea as potential military cargo carriers, Ukraine said it opened maritime routes for civilian vessels from several southern ports.

Ukrainian Navy spokesman Oleg Chalyk said a first ship would take the newly open route "in the near future."