WASHINGTON, Sept 12 (Reuters) – Russia has largely ceded its gains near Kharkiv and many of its withdrawing Russian troops have left Ukraine, moving the border back to Russia, a senior U.S. military official said on Monday. As they retreat, the United States has seen anecdotal reports of Russian forces abandoning their equipment, “which could be indicative of disorganized Russian command and control,” said a US military official, speaking on condition of anonymity. The statements to Pentagon reporters followed a weekend of rapid gains for Ukrainian forces. Ukraine’s general staff said its troops had recaptured more than 20 towns and villages in the past day alone, as Ukrainian forces pushed deeper into territory seized by fleeing Russian troops. Sign up now for FREE unlimited access to Reuters.comSign up The US military official was optimistic, but cautious, when he described the Ukrainian advances. “It’s clear they are fighting hard,” the official said, citing progress in the south and east to retake territory. Ukraine said it had repelled attempted Russian advances in two key areas of the Donetsk region – the city of Bakhmut and Mayorsk, near the coal-producing town of Horlivka, the general staff said in an evening briefing. However, the senior US 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 Gadchev, the Russian-installed head of Moscow’s occupation administration in what remains of Russian territory in the Kharkiv region, acknowledged that Ukrainian forces had entered the border. The official did not say how many withdrawing Russian forces left Ukrainian soil and crossed into Russia, but described a significant retreat. “On the ground near Kharkiv we estimate that Russian forces have largely ceded their gains to the Ukrainians and withdrawn north and east. Many of these forces have moved across the border into Russia,” the official said. Sign up now for FREE unlimited access to Reuters.comSign up Report by Phil Stewart and Idrees Ali. Edited by Jonathan Oatis and Lisa Shumaker Our Standards: The Thomson Reuters Trust Principles. Idrees Ali Thomson Reuters National Security Correspondent focusing on the Pentagon in Washington Reports on US military activity and operations around the world and their impact. He has reported from over 22 countries including Iraq, Afghanistan and much of the Middle East, Asia and Europe. From Karachi, Pakistan.