Russia claims to have taken control of 97 per cent of one of the two provinces that make up Ukraine's Donbas, bringing the Kremlin closer to its goal of fully capturing the eastern industrial heartland of coal mines and factories.

Russian Defence Minister Sergei Shoigu said Moscow's forces hold nearly all of Luhansk province. And it appears that Russia now occupies roughly half of Donetsk province, according to Ukrainian officials and military analysts.

After abandoning its bungled attempt to storm Kyiv two months ago, Russia declared that taking the entire Donbas is its main objective. Moscow-backed separatists have been battling Ukrainian Government forces in the Donbas since 2014, and the region has borne the brunt of the Russian onslaught in recent weeks.

Early in the war, Russian troops also took control of the entire Kherson region and a large part of the Zaporizhzhia region, both in the south. Russian officials and their local appointees have talked about plans for those regions to either declare their independence or be folded into Russia.

An unexploded Russian rocket embedded in a field near Soledar, eastern Ukraine. Photo / Bernat Armangue, AP

But in what may be the latest instance of anti-Russian sabotage inside Ukraine, Russian state media said an explosion at a cafe in the city of Kherson wounded four people. Tass called the apparent bombing in the Russian-occupied city a "terror act".

Before the February 24 invasion, Ukrainian officials said Russia controlled about 7 per cent of the country, including the Crimean Peninsula, which Russia annexed in 2014, and areas held by the separatists in Donetsk and Luhansk. Last week, Ukrainian President Volodymyr Zelenskyy said Russian forces hold 20 per cent of the country.

Russia has superior firepower but the Ukrainian defenders are entrenched and have shown the ability to counterattack.

At the same time as insisting on Ukraine's need to defeat Russia on the battlefield, Zelenskyy said at a Financial Times conference that he is still open to peace talks with Russian President Vladimir Putin.

But a former senior US intelligence officer said the time isn't right.

A Ukrainian serviceman pauses before going back to the frontline in the Donetsk region, eastern Ukraine. Photo / Bernat Armangue, AP

"You're not going to get to the negotiating table until neither side feels they have an advantage that they could push," said Andrea Kendall-Taylor of the Washington-based Centre for a New American Security.

The Russians "think they will be able to take the whole of the Donbas and then might use that as the opportunity to call for negotiations," Kendall-Taylor said at an online seminar organised by Columbia and New York universities.

Shoigu, the Russian defence minister, said Moscow's forces have seized the residential quarters of Sievierodonetsk and are fighting to take control of an industrial zone on the city's outskirts and nearby towns.

Sievierodonetsk and nearby Lysychansk have seen heavy fighting in recent weeks. They are among a few cities and towns in the Luhansk region still holding out against the Russian invasion, which is being helped by local pro-Kremlin forces.

Shoigu added that Russian troops were pressing their offensive toward the town of Popasna and had taken control of Lyman and Sviatohirsk and 15 other towns in the region.

Ukrainian presidential adviser Mykhailo Podolyak urged his people not to be downhearted about the battlefield reverses.

"Don't let the news that we've ceded something scare you," he said in a video address. "It is clear that tactical manoeuvres are ongoing. We cede something, we take something back."

Luhansk governor Serhiy Haidai conceded that Russian forces control the industrial outskirts of Sievierodonetsk.

Civilian militia men hold shotguns during training at a shooting range on the outskirts of Kyiv. Photo / Natacha Pisarenko, AP

"The toughest street battles continue, with varying degrees of success," Haidai said. "The situation constantly changes, but the Ukrainians are repelling attacks."

Moscow's forces also kept up their artillery barrage of Lysychansk. Haidai said Russian troops shelled a market, a school, and a college building, destroying the latter. At least three people were wounded, he said.

"A total destruction of the city is under way. Russian shelling has intensified significantly over the past 24 hours. Russians are using scorched-earth tactics," Haidai said.

Meanwhile, the US military has begun training Ukrainian forces on the sophisticated multiple rocket launchers that the Biden administration agreed last week to provide. The Pentagon said the training is going on at a base in Germany and elsewhere in Europe.

The High Mobility Artillery Rocket System, or HIMARS, is mounted on a truck and can carry a container with six rockets, which can travel about 70km. Officials said it would take about three weeks of training before they could go to the battlefront.

The war also brought a standoff Tuesday between the head of the UN nuclear watchdog agency and Ukrainian authorities over the biggest nuclear power plant in Europe.

The director of the International Atomic Energy Agency, Rafael Mariano Grossi, wants to visit the Zaporizhzhia plant to help maintain its safety after it was taken by Russian troops in March.

But Energoatom, the Ukrainian state company overseeing the country's nuclear plants, said that Grossi isn't welcome. It said his planned tour is "yet another attempt to legitimise the occupier's presence there".

Amid fears of a global food crisis because of the war, the Kremlin said Ukraine needs to remove sea mines near its Black Sea port of Odesa to allow essential grain exports to resume. Ukrainian officials have expressed concern that removing the mines could enable Moscow's forces to attack.

- John Leicester & Hanna Arhirova of AP