Russia pummelled towns and villages in Ukraine's northeastern Kharkiv region on Monday, days after launching a surprise ground offensive over the border that has forced thousands to evacuate. 

The Ukrainian army acknowledged Russia was "achieving tactical success" after launching a ground assault on Friday that has sparked the evacuation of almost 6,000 people. 

But President Volodymyr Zelensky stressed Ukraine had sent in reinforcements, and that a "counterattack" was ongoing.

"Our task is clear: to thwart Russia's attempt to expand the war," he said in an evening address. 

Russia's defense ministry said its troops had "improved the tactical position and dealt a blow to (Ukrainian) manpower" around border villages, including Lyptsi, and the town of Vovchansk. 

Kateryna Stepanova, 74, who fled Lyptsi with her son, said several bombs had hit her street. 

"We weren't going to leave... but now this. Thankfully, we're alive," she said, sitting in a minibus at a gathering point for evacuees. 

"It's such a horror what's going on there. The houses are on fire!"

"They are shelling the villages, firing everything they can," Sergiy Kryvetchenko, deputy head of the Ukrainian military administration in Lyptsi, told AFP.

"The KABs (guided aerial bombs) are flying. The artillery is flying. Drones. Everything," he said.

Guided aerial bombs are falling "like rain" said one serviceman, who was resting after fending off Russian assaults in Lyptsi.

Ukraine's security council chief Oleksandr Lytvynenko said Moscow had mounted tens of thousands of troops against Kharkiv region.

"There are a lot of Russians, quite a lot. About 50,000 were on the border. Now there are much more than 30,000 coming," he told AFP.

Children taken to safety

Kharkiv regional governor Oleg Synegubov said 5,762 people had been evacuated so far since the start of the offensive. 

"Today we plan to bring out around 1,600 local residents," he added.

He also said it was necessary to move 113 children to safety from state children's homes near the border. 

The General Staff said that in the Kharkiv region, Russia "does not cease offensive actions", carrying out 11 attacks on Monday, two of them ongoing, and launching eight air strikes. 

It said Russia had "partial success" in capturing the village of Lukyantsi but Ukraine halted its advance.

Synegubov said Russia had struck "more than 30" towns and villages with artillery and mortars. 

On Monday evening, a missile hit Korotych, a settlement near the city of Kharkiv, killing a 38-year-old man and injuring three, police said. 

Earlier attacks injured a 71-year-old woman in Lyptsi and a man, 69, in the town of Izyum, the governor said. 

Ukraine's army reported fighting in Vovchansk, where Russia was deploying "significant forces", numbering up to five battalions. 

Vovchansk suffered "massive shelling" on Sunday, said Synegubov. 

In the southern Kherson region, two people were found dead after a strike hit a residential building, regional military administration chief Oleksandr Prokudin said. 

Ukraine launched drone strikes on western Russia, a security source in Kyiv told AFP, hitting an oil terminal in the Belgorod border region and an electrical substation in the Lipetsk region. 

Regional authorities in Russia's Kursk border region said one woman was killed and three wounded when a drone struck several cars.

'Expanding' front line

Kyiv and Moscow have been targeting each other's energy infrastructure and Ukraine's generation facilities have been severely damaged. 

Rockets struck the Lugansk region of eastern Ukraine under Russia's control, according to Moscow-appointed governor Leonid Pasechnik. 

The attack on an industrial zone of the town of Sorokyne, known as Krasnodon in Russian, killed three and injured four, he said. 

In the Kharkiv region, "the grey zone and the front line are expanding" because Russia is "trying to deliberately stretch it, attacking in small groups in new directions", governor Synegubov said. 

The DeepState Telegram channel — which is close to the Ukrainian army — said Russia had taken some 100 square kilometres (39 square miles). 

Russia "continues to advance to Vovchansk", the channel said. "They are gaining a foothold on the outskirts for further entry into the town." 

Russia was also advancing towards Lyptsi and trying to enter nearby Glyboke, it said.

Ukraine was mounting "constant fire", including from drones, "but unfortunately it does not stop them". 

Rybar, a Russian Telegram channel with military links, said Moscow's offensive led to territorial gains because troops took some villages where Russian soldiers already had a presence and others that were "deserted wastelands".