* Ukraine redirecting Russia gas to Europe
* Ukraine counter-offensive could shift war's momentum
* Ukrainian forces seeking to cut off Russian supply lines
* U.S. concerned about future course of war
KHARKIV, Ukraine, May 11
Flows of Russian gas to Europe through a key transit point in Ukraine dried up on Wednesday, while Kyiv claimed battlefield gains over invading Russian forces, including the recapture of four villages around the second city of Kharkiv.
Ukraine has remained a major route for Russian gas to Europe even after President Vladimir Putin ordered what he called a "special military operation" on Feb. 24.
Mounting Western sanctions are seeking to ban or phase out the use of Russian energy, a major source of funds for Putin's war effort and a vulnerability for Europe, especially Germany.
Blaming the interference of Russian occupying forces for the suspension, Ukraine's gas operator said on Tuesday it would redirect gas from the Sokhranivka transit point, which is in an area occupied by Russian forces, to another in a Ukraine-controlled area.
Early Wednesday data from the network operator showed zero nominations for Russian gas through the transit point.
Since Russia was forced to abandon an assault on the capital Kyiv at the end of March, its main force has been trying to encircle Ukrainian troops in the eastern Donbas region, using the city of Izyum near Kharkiv, in the northeast, as a base.
Ukrainian troops have mostly held out against assaults from three directions, and top U.S. intelligence officials say the war is now at a stalemate.
Putin appeared to be preparing for a long conflict, and a Russian victory in the Donbas region might not end the war, U.S. Director of National Intelligence Avril Haines said in Washington on Tuesday.
But the counterattack near Kharkiv could signal a new phase, with Ukraine going on the offensive and supply lines into Russia now potentially vulnerable.
President Volodymyr Zelenskiy said Ukrainian successes were gradually pushing Russian forces out of Kharkiv, which has been under bombardment since the war began.
"But I also want to urge all our people ... not to spread excessive emotions. We should not create an atmosphere of excessive moral pressure, where victories are expected weekly and even daily," Zelenskiy said in a video address.
In the villages of Staryi Saltiv and Vilkhivka near Kharkiv, Ukrainian servicemen gathered the bodies of Russian soldiers who were killed in the fighting, according to Reuters witnesses.
Russian forces were trying to prevent Ukrainian troops from moving further towards the border in the Kharkiv region and were trying to fully take over the town of Rubizhne, Ukraine's general staff said early on Wednesday.
Ukrainian border guards reported Russian forces were shelling Sumy and Chernihiv regions close to the border.
"Enemy aircraft twice launched non-guided missiles on border areas of Sumy. There were also two instances of mortar shelling in Chernihiv region," they said on their Telegram channel.
In the south, Ukrainian armed forces said they struck nine enemy targets, with enemy losses of 79 servicemen and 12 pieces of equipment, including armoured vehicles and howitzers.
Russian fire was concentrated on the Mykolaiv region where private homes were damaged as well as farms and power lines to one town.
Russian forces continued to pummel the Azovstal steelworks in the southern port of Mariupol with artillery, tanks and aircraft bombing, Ukraine's general staff said, trying to capture the last bastion of Ukrainian resistance in the ruined city.
Ukraine says tens of thousands of people have been killed in the city under two months of Russian siege.
Russia was trying to reinforce exposed troops on Zmiinyi Island, also known as Snake Island, which became famous for the foul-mouthed defiance of Ukrainian border guards early in the invasion.
"If Russia consolidates its position on Zmiinyi Island with strategic air defence and coastal defence cruise missiles, they could dominate the northwestern Black Sea," the British Ministry of Defence said in a regular bulletin.
Russia's resupply vessels have minimum protection in the western Black Sea, following the Russian navy's retreat to Crimea after the loss of the flagship Moskva, it said.
Reuters was unable to independently verify the reports of fighting.
The number of Ukrainians who have fled their country is approaching 6 million, according to the United Nations, which says the refugee crisis is the fastest growing since World War Two.
Russia denies targeting civilians and rejects Ukrainian and Western allegations of war crimes.