KOROVII YAR, Ukraine — After months of grueling artillery battles spent desperately holding their lines under punishing Russian aerial and artillery bombardment, Ukrainian troops are enjoying a sudden rush of conquest in northeastern Ukraine.
“The Russians have been retreating. We broke their lines and have been pursuing them since,” said Rob Roy, a 26-year-old American volunteer who uses the code name Borys. He was piled into the back of an army truck along with a company of Ukrainian and foreign soldiers who were in an ebullient mood, heading down the road to new positions toward the town of Lyman.
“Basically,” he added, “we shattered them.”
Ukraine’s lightning counteroffensive in the northeast has reclaimed vast swaths of territory including Lyman, a crucial railway hub in Donetsk — one of the four Ukrainian regions that President Vladimir V. Putin of Russia said last week his country was annexing and treating as its own.
Although progress has been slower in the south, the northeastern offensive has forced Russian troops to flee Lyman and move to reinforce their lines 25 miles to the south around the city of Bakhmut.
Behind them, Ukrainian Army units including Mr. Roy’s Karpatska Sich battalion are on the move across a wide expanse of rolling hills and forests east and south Izium, the last major prize the offensive captured before Lyman. They are camping in forests and small hamlets, setting up firing positions on ridges, and clearing towns and villages as Ukrainian airborne troops spearhead the advance.
Mr. Roy said his light infantry unit of international and Ukrainian volunteers, now formally integrated into the Ukrainian Army, captured two Russian soldiers Sunday in the small farming town of Karovii Yar.
The Russians were found asleep inside a building, apparently left behind in the rushed retreat of the last 20 days. But the men were armed and had rounds in the chambers of their assault weapons, he said, showing photos on his cellphone of two men on the ground with their hands bound and eyes bound with tape.
“They gave several hours of good intelligence,” Mr. Roy said. The prisoners were then handed over to other Ukrainians and taken away.
Ukrainian soldiers — and civilians who were lining up by trucks to receive handouts of food and milk — said they were surprised by the Russians’ sudden pullback.
Captain Ihor Nazarenko, 55, a tank commander who had parked beside the road, roared with laughter at the rapid retreat. “They are running, and we are running after them,” he said.
Mr. Roy said the fighting was heavy until just recently, even after Ukrainian troops broke through into Izium. Low-flying Russian jets bombed close to their positions 11 days ago, he said.
“They did not need to pull back,” he said of the Russians. “They were firing on us two days ago.”
But many of the Russian conscripts were in poor shape, he said.
“Lots of times they were wearing flip-flops, malnourished,” he said. Two Russian soldiers his unit found had only one gun between them, and were carrying a pack of food and two drums of water, he said.
At another abandoned Russian position, he said, they found graffiti apparently left behind by fleeing soldiers that used a slur to describe their commander.
“It does not scream of a well mobilized army,” he said. “My feeling is they don’t want to be here.”
— Carlotta Gall, Oleksandr Chubko and Ivor Prickett