Russian shelling has killed at least seven people in Ukraine over the past 24 hours and wounded 25 more, Ukrainian officials said.

The country's presidential office said Russian forces targeted cities and villages in southeast Ukraine, with most civilian casualties occurring in Donetsk province, where Russia stepped up its offensive in recent days.

Governor Pavlo Kyrylenko said in a Telegram post two people died in the city of Avdiivka, which is located in the centre of the province, and the Donetsk cities of Sloviansk, Krasnohorivka and Kurakhove each reported one civilian killed.

"Every crime will be punished," he wrote.

Mr Kyrylenko urged the province's more than 350,000 remaining residents to flee late on Tuesday, saying evacuating Donetsk is necessary to save lives and allow the Ukrainian army to put up a better defence against the Russian advance.

Donetsk is part of the Donbas, a mostly Russian-speaking industrial area where Ukraine's most experienced soldiers are concentrated.

Russian President Vladimir Putin on Monday declared the complete seizure of the region's other province, Luhansk, after Ukrainian troops withdrew from the last city under their control.

Luhansk governor Serhiy Haidai on Wednesday denied that the Russians have completely captured the province.

Heavy fighting continued in villages around Lysychansk, the city Ukrainians soldiers withdrew from and which Russian troops took on Sunday, he said.

"The Russians have paid a high price, but the Luhansk region is not fully captured by the Russian army," Mr Haidai said.

"Some settlements have been overrun by each side several times already."

He said up to 15,000 residents remain in Lysychansk and some 8,000 in the nearby city of Sievierodonetsk, which Russian and separatist fighters seized last month.

Pro-Russian separatists have fought Ukrainian forces and controlled much of the Donbas for eight years.

Before Russia invaded Ukraine on February 24, Mr Putin recognised the independence of the two self-proclaimed separatist republics in the region.

Since Russian forces failed to make inroads in capturing Kyiv, Ukraine's capital, Moscow has concentrated its offensive on seizing the remaining Ukrainian-held areas of the Donbas.

To the north of Donetsk, Russian forces also hit Kharkiv, Ukraine's second-largest city, with missile strikes overnight, the Kharkiv regional governor said on Wednesday on Telegram.

Three districts of the city were targeted, governor Oleh Syniehubov said.

Three people, including a toddler, sustained injuries, according to the governor.

A university building and an administrative building were destroyed.

In other developments European Commission chief Ursula von der Leyen has said the European Union needs to make emergency plans to prepare for a complete cut-off of Russian gas in the wake of the Kremlin's war in Ukraine.

The EU has already imposed sanctions on Russia, including on some energy supplies, and is moving away from Kremlin-controlled deliveries - but Ms von der Leyen said the 27-member bloc needs to be ready for shock disruptions coming from Moscow.

"We also need to prepare now for further disruption of gas supply and even a complete cut-off of Russian gas supply," Ms von der Leyen told the EU legislature in Strasbourg, France.

She said a dozen members have already been hit by reductions or full cuts in gas supplies as the political stand-off with Moscow over the Ukraine invasion intensifies.

"It is obvious: Putin continues to use energy as a weapon. This is why the Commission is working on a European emergency plan," she said.

"We need to make sure that in case of full disruption, the gas flows towards where it is most needed. We have to provide for European solidarity."

European Union countries already agreed last month that all natural gas storage in the 27-nation bloc should be topped up to at least 80% capacity for next winter to avoid shortages during the cold season.

The new regulation also says underground gas storage on EU soil will need to be filled to 90% capacity before the 2023-24 winter.

The war in Ukraine has prompted the 27-nation bloc to rethink its energy policies and sever ties with Russian fossil fuels.

Member countries have agreed to ban 90% of Russian oil by year-end in addition to a ban on imports of Russian coal that will start in August.

The EU has not included gas - a fuel used to power factories and generate electricity - in its own sanctions for fear of seriously harming the European economy.

Before the war in Ukraine, it relied on Russia for 25% of its oil and 40% of its natural gas.

To slash its use of Russian energy, the European Commission has been diversifying suppliers.

"And our efforts are already making a big difference," Ms von der Leyen said.

"Since March, global LNG exports to Europe have risen by 75% compared to 2021. LNG exports from the US to Europe have nearly tripled."

In the meantime, the average monthly import of Russian pipeline gas is declining by 33% compared with last year, Ms von der Leyen said, as she called for a speedy transition toward renewable sources of energy.

"Some say, in the new security environment after Russia's aggression, we have to slow down the green transition. This transition would come at the 'the cost of basic security', they say. The opposite is true.

"If we all do nothing but compete about limited fossil fuels, the prices will further explode and fill Putin's war chest.

"Renewables are home-grown. They give us independence from Russian fossil fuels. They are more cost-efficient. And they are cleaner."

The EU Council agreed last month to raise the share of renewables in the bloc's energy mix to at least 40% by 2030 - up from the previous target of 32%. In addition, a 9% energy consumption reduction target for 2030 will become binding on all EU member states for the first time.