ZAPORIZHZHIA, Ukraine — Ukrainian forces have advanced by about a mile at some parts of the front line near the eastern city of Bakhmut, the military said on Saturday, claiming a gain in one of three battles underway now as Ukraine’s counteroffensive takes shape in the country’s southeast.
The Ukrainian military went on the attack near Bakhmut to take advantage of a rotation of Russian units in the area, Col. Serhiy Cherevaty, the spokesman for the eastern military command, told local television. He said the Ukrainian military had been in six engagements near Bakhmut over the past 24 hours.
He did not specify where Ukraine had pressed forward, and his claims could not be independently verified. Moscow’s forces say they are repelling Ukrainian attacks in three areas that have been the focus of fighting as the counteroffensive gets underway, and Russian state news said that Ukrainian forces had been unsuccessful in their attempts to retake Bakhmut territory.
Ukrainian troops are fighting in fields and in grassy, rolling hills to the west of Bakhmut, having been mostly pushed from the city last month after the longest and bloodiest battle of the war.
With Russia having presented the city’s capture as a victory, it must now defend it or risk an embarrassing setback. Ukraine’s objective in Bakhmut, military analysts and Ukrainian officers have said, is to compel Russia to divert troops from elsewhere in southern Ukraine to defend the ruins of Bakhmut, and to inflict casualties.
“Our main goal remains unchanged,” Mr. Cherevaty said: “to inflict maximum damage on the enemy.”
To the southwest of Bakhmut, Ukraine is fighting in two locations that are considered central to its broader counteroffensive goal of severing Russian rail and road links that connect Russia to the occupied Crimean Peninsula. The battles near the towns of Orikhiv in the Zaporizhzhia region and Velyka Novosilka in the Donetsk region broke out over the past week. Ukrainian officials have not commented on fighting in these areas.
U.S. officials, speaking on the condition of anonymity to discuss critical military operations, have confirmed that Ukrainian troops, as expected, suffered casualties and equipment losses in the early fighting. Russian losses are unclear, but attackers typically suffer heavier initial casualties than dug-in defenders.
Russian military bloggers were already taking early victory laps, praising the military for what they described as holding the line against an onslaught of Ukrainian forces backed by the strength of NATO.
The Russian state news Channel 1 reported that Russian forces had repelled Ukrainian attacks near Lysychansk and Avdiivka, and said that Ukrainian forces were “regularly failing” in their attempts to break into Bakhmut, which Russian news outlets still call its Soviet name, Artemivsk.
Videos and photos posted by pro-war Russian bloggers, and verified by The New York Times, show that at least three German-made Leopard 2 tanks and eight American-made Bradley fighting vehicles were recently abandoned by Ukrainian troops or destroyed. And Sasha Kots, a Russian military blogger, said on Telegram that captured German-made tanks would be a “trump card in the information war.”
As the fighting escalates along the front, the two armies are also firing long-range rockets, missiles and drones at targets far away.
Overnight into Saturday, Russian ballistic and cruise missiles and exploding drones struck a Ukrainian military airfield near Poltava, to the east of Kyiv, said Dmytro Lunin, the head of the region’s military administration. Mr. Lunin said that the strike had started fires and damaged equipment, but that no one was killed or wounded.
In Russian-occupied territory, an explosion damaged a resort complex on the Sea of Azov where Russian forces were quartered, Ivan Fedorov, the mayor of the city of Melitopol, told the local news media. Russian forces later evacuated the site, he said.
