KYIV, Ukraine >> Russian troops were withdrawing from around Ukraine’s second-largest city after bombarding it for weeks, the Ukrainian military said Saturday, as Kyiv and Moscow’s forces engaged in a grinding battle for the country’s eastern industrial heartland.

Ukraine’s military said the Russian forces were pulling back from the northeastern city of Kharkiv and focusing on guarding supply routes, while launching mortar, artillery and airstrikes in the eastern province of Donetsk in order to “deplete Ukrainian forces and destroy fortifications.”

Defense Minister Oleksii Reznikov said Ukraine was “entering a new — long-term — phase of the war.”

In a show of support, a U.S. Senate delegation led by Minority Leader Mitch McConnell met with Ukrainian President Volodymyr Zelenskyy on Saturday in Kyiv. A video posted on Zelenskyy’s Telegram account showed McConnell, who represents the state of Kentucky, and fellow Republican senators Susan Collins of Maine, John Barrasso of Wyoming and John Cornyn of Texas greeting him.

Their trip came after Kentucky’s other senator, Rand Paul, blocked until next week Senate approval of an additional $40 billion to help Ukraine and its allies withstand Russia’s three-month-old invasion. In a statement after leaving Ukraine, McConnell said the United States “stands squarely behind Ukraine and will sustain our support until Ukraine wins this war.”

After failing to capture Kyiv following the Feb. 24 invasion, Russian President Vladimir Putin has shifted his focus eastward to the Donbas, an industrial region where Ukraine has battled Moscow-backed separatists since 2014.

The offensive aims to encircle Ukraine’s most experienced and best-equipped troops, who are deployed in the east, and to seize parts of the Donbas that remain in Ukraine’s control.

Airstrikes and artillery barrages make it extremely dangerous for journalists to move around in the east, hindering efforts to get a full picture of the fighting. But it appears to be a back-and-forth slog without major breakthroughs on either side.

Russia has captured some Donbas villages and towns, including Rubizhne, which had a prewar population of around 55,000.

Zelenskyy said Ukraine’s forces have also made progress in the east, retaking six towns or villages in the past day. In his nightly address Saturday, he said “the situation in Donbas remains very difficult” and Russian troops were “still trying to come out at least somewhat victorious.”

“Step by step,” Zelenskyy the president said, “we are forcing the occupants to leave the Ukrainian land.”

Kharkiv, which is near the Russian border and only 80 kilometers (50 miles) southwest of the Russian city of Belgorod, has undergone weeks of intense shelling. The largely Russian-speaking city with a prewar population of 1.4 million was a key military objective earlier in the war, when Moscow hoped to capture and hold major cities.

Ukraine “appears to have won the Battle of Kharkiv,” the Institute for the Study of War, a Washington-based think tank, said. “Ukrainian forces prevented Russian troops from encircling, let alone seizing Kharkiv, and then expelled them from around the city, as they did to Russian forces attempting to seize Kyiv.”

Regional Gov. Oleh Sinegubov said via the Telegram messaging app that there had been no shelling attacks on Kharkiv in the past day.

He added that Ukraine launched a counteroffensive near Izyum, a city 125 kilometers (78 miles) south of Kharkiv that has been held by Russia since at least the beginning of April.

Fighting was fierce on the Siversky Donets River near the city of Severodonetsk, where Ukraine has launched counterattacks but failed to halt Russia’s advance, said Oleh Zhdanov, an independent Ukrainian military analyst.

“The fate of a large portion of the Ukrainian army is being decided — there are about 40,000 Ukrainian soldiers,” he said.

However, Russian forces suffered heavy losses in a Ukrainian attack that destroyed a pontoon bridge they were using to try to cross the same river in the town of Bilohorivka, Ukrainian and British officials said.

Britain’s defense ministry said Russia lost “significant armored maneuver elements” of at least one battalion tactical group in the attack. A Russian battalion tactical group consists of about 1,000 troops.

The ministry said the risky river crossing was a sign of “the pressure the Russian commanders are under to make progress in their operations in eastern Ukraine.”

Zelenskyy has warned of a global food crisis as Russia blockades Ukrainian grain from leaving port.

The Group of Seven leading economies echoed that Saturday, saying that “Russia’s war of aggression has generated one of the most severe food and energy crises in recent history, which now threatens those most vulnerable across the globe.”

Putin launched the war in Ukraine aiming to thwart NATO’s expansion in Eastern Europe.

But the invasion has other countries along Russia’s flank worried they could be next, and this week the president and prime minister of Finland said they favor seeking NATO membership. Officials in Sweden are expected to announce a decision Sunday on whether to apply to join the Western military alliance.

In a phone call Saturday, Putin told Finnish President Sauli Niinisto that there are no threats to Finland’s security and joining NATO would be an “error” and “negatively affect Russian-Finnish relations.”

The Kremlin said the two leaders had a “frank exchange of views.”

Niinisto said the discussion “was straightforward and unambiguous and was held without exaggeration. Avoiding tensions was considered important.”

Russian Deputy Foreign Minister Alexander Grushko said accession to NATO by Finland and Sweden would heighten security tensions in the Arctic, “turning it into an arena of military competition.”

Russian energy group Inter RAO suspended deliveries of electricity to Finland on Saturday, according to a statement from the Finnish national electrical grid operator. But only around 10% of Finland’s electricity comes from Russia, and authorities did not expect shortages.

The Nordic nations’ potential bids were thrown into question Friday when Turkish President Recep Tayyip Erdogan said his country is “not of a favorable opinion.”

U.S. Secretary of State Antony Blinken was scheduled to meet his NATO counterparts, including Turkey’s foreign minister, this weekend in Germany.

In other developments:

— Ukrainian fighters holed up in a steel plant in the ruined southern port of Mariupol faced continued attacks on the city’s last stronghold of resistance. Ukrainian Deputy Prime Minister Iryna Vereshchuk said authorities were negotiating the evacuation of 60 severely wounded troops, but Russia had not agreed to the evacuation of all wounded fighters at the steelworks, who number in the hundreds.

— Performing in the final of the hugely popular Eurovision Song Contest, Ukrainian band Kalush Orchestra made an impassioned plea for help for those inside the steel plant. The band later emerged the event’s winner early Sunday. Zelenskyy signaled that he was watching from Kyiv, saying in a statement, “This is not a war, but nevertheless, for us today, any victory is very important.″

— An adviser to Mariupol Mayor Petro Andryushenko said via Telegram that a convoy of between 500 and 1,000 cars carrying civilians from the city was allowed to enter Ukraine-controlled territory and was headed for Zaporizhzhia, the first major city beyond the front lines.

— The deputy speaker of Russia’s parliament, Anna Kuznetsova, visited Kherson, a region bordering the Black Sea that has been held by Russia since early in the war. Russia has installed a pro-Moscow regional administration, and Britain’s defense ministry said Russia could stage a local referendum on joining Russia with results likely manipulated to show majority support.

— Zelenskyy signed into law a measure allowing for the banning of political parties found to be supporting or defending Russia’s invasion, the head of the national parliament’s legal policy committee reported.