There were no US or North Atlantic Treaty Organisation fatalities; however, one Afghan soldier was killed and another wounded, according to the statement.
Analysts say such attacks are expected to increase this year as USA troops engage with the Afghan military to double the size of its special forces, considered to be effective in the fight against insurgents.
Taliban spokesman Zabihullah Mujahid was quoted by Reuters as saying that over 100 policemen were killed or wounded.
An Afghan soldier shot and injured seven USA soldiers in an apparent inside attack at a military base in northern Afghanistan on Saturday, a military official said.
The attack took place in the Afghan National Army 209th Corps headquarters at Camp Shaheen, in the northern city of Mazar-e-Sharif.
The Taliban in a statement did not say if they were directly behind the attack, only crediting a "patriotic Afghan soldier" for the assault. The others held out against Afghan special forces that had responded to the attack, he said. The attack Saturday at Camp Shaheen left seven American soldiers wounded, according to officials with the NATO-led mission in the country.More news: Trump offers to help resolve Gulf crisis, UAE tightens squeeze on Qatar
Nine police officers and 13 civilians were wounded, he said.
In the deadliest attack in Achin in eastern Nangarhar province, three US soldiers were killed when an Afghan soldier emptied his automatic rifle in their direction.
After more than 15 years of war the Taliban control broad swaths of the country and the struggling Afghan security forces continue to take an nearly unsustainable amount of casualties as they battle to hold provincial capitals. The Taliban stormed a police headquarters in eastern Afghanistan on Sunday after striking it with two suicide auto bombs, killing at several police officers, officials said. The Taliban claimed responsibility for the attack. Without calling for the operation, the Taliban fighting against the Kabul regime and the forces behind it have reported it and described the soldier as a "patriot".
No US military troops were killed, the mission said in a statement.
So far this year, six USA troops have been killed by hostile fire in Afghanistan.
Nevertheless, these attacks fueled a strong sense of mistrust between the coalition soldiers and the Afghan military.
He said an Afghan commando opened fire at the North Atlantic Treaty Organisation forces, resulting in casualties.