By Phil Stewart and Idrees Ali
WASHINGTON (Reuters) -Russia has largely ceded its gains near Kharkiv and many of the withdrawing Russian soldiers have exited Ukraine, moving over the border back into Russia, a senior U.S. military official said on Monday.
As it pulls back, the United States has seen anecdotal reports of Russian forces abandoning their equipment, "which could be indicative of Russia's disorganized command and control," the U.S. military official said, speaking on condition of anonymity.
The remarks to Pentagon reporters followed a weekend of rapid gains for Ukrainian forces. Ukraine's general staff said its soldiers had recaptured more than 20 towns and villages in just the past day, as Ukrainian forces swept deeper into territory seized from fleeing Russian troops.
The U.S. military official was upbeat, but cautious, when describing the Ukrainian advances.
"It's clear they're fighting hard," the official said, citing progress in the south and east to reclaim territory.
Ukraine said it repelled attempted Russian advances in two important areas of the Donetsk region - the city of Bakhmut and Maiorsk, near the coal-producing town of Horlivka, the general staff said in an evening update.
But the senior U.S. military official said Russia was still focusing its firepower on Bakhmut.
"We continue to see heavy use of artillery and airstrikes," the official said, speaking on condition of anonymity.
Vitaly Ganchev, the Russian-installed head of Moscow's occupation administration in what remained of Russian-held territory in the Kharkiv region, acknowledged that Ukrainian forces had broken through to the frontier.
The official did not say how many withdrawing Russian forces had left Ukrainian territory and exited to Russia but described a significant pullback.
"On the ground in the vicinity of Kharkiv we assess that Russian forces have largely ceded their gains to the Ukrainians and have withdrawn to the north and east. Many of these forces have moved over the border into Russia," the official said.