"Ghazni City remains under Afghan government control", Lt. Col. Martin O'Donnell, a spokesman for Operation Resolute Support and U.S. Forces Afghanistan, told Military.com on Tuesday.
The Afghan military has made significant gains against the Taliban in Ghazni city.
Rahmani said the base fell to the Taliban after the soldiers, who had resisted the three-day onslaught, failed to get any reinforcements and ran out of ammunition, food and water. Rahmani said 43 troops were killed and wounded.
"What we observed, as these Afghan-led operations drove a large portion of Taliban from the city over the last day or so, was the retreating Taliban attacking the more vulnerable surrounding districts, which Afghan forces are reinforcing".
Meanwhile, the Taliban spokesman Qari Yosuf Ahmadi has tweeted that the military base in Chilgazi area of the district was taken over by the militant group.
An Afghan Army soldier keeps watch at a checkpoint in Ghazni. He said eight military Humvees were also seized.
At least seven Afghan police soldiers were killed in a clash with Taliban insurgents on Tuesday on the Kabul-Kandahar highway in Zabul province, local officials said Wednesday.
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The attack came as the situation in the embattled central city of Ghazni eased after the Taliban said they had ordered forces out after five days of fighting that killed and wounded hundreds and left the city a burned-out wreck. The Taliban quickly denied they were involved.
Government forces, backed by United States air strikes, now appear to have pushed fighters out of the eastern city.
Tens of thousands of residents have been trapped inside the strategic provincial capital since more than 1,000 Taliban militants overran its defences in a pre-dawn assault on Friday.
The United States and North Atlantic Treaty Organisation have launched airstrikes and sent military advisers to aid Afghan forces as they fight for the city, just 120 kilometres from the Afghan capital with a population of some 270,000 people.
The Taliban also destroyed a telecommunications tower on the city outskirts, cutting off landline and cellphone links to the city.
The fighting brought civilian life in the city to a standstill, and also severely damaged Ghazni's historic neighborhoods and cultural treasures. But he said wounded people are still arriving at the city's only hospital, which has been overwhelmed by the casualties. Afghan forces repelled the initial assault and in recent days have struggled to flush the insurgents out of residential areas where they are holed up.
The U.S. and North Atlantic Treaty Organisation formally concluded their combat mission in Afghanistan at the end of 2014, but have since then repeatedly come to the aid of Afghan forces as they struggle to combat the resurgent Taliban.