"The main focus of Operation Mansouri will be on foreign forces, their military and intelligence infrastructure and in eliminating their internal mercenary apparatus", it said.
At least 10 militants launched an attack on a base in northern Balkh province last Friday, storming it in three military vehicles.
United States officials say a solution to the conflict can only come through a political settlement which includes the Taliban, who have rejected peace talks while foreign forces remain in Afghanistan.
Already beset by killings, desertions, and struggles over leadership and morale, Afghan forces have been straining to beat back insurgents since US-led North Atlantic Treaty Organisation troops ended their combat mission in December 2014.
Two US service members were killed during an operation against Islamic State militants in eastern Afghanistan overnight on Wednesday, US officials said on Thursday, as President Donald Trump's administration looks to craft a strategy in the war-torn country.
The operation, which forced the defence minister and army chief of staff to resign, was a stark illustration of the struggle facing Western-backed Afghan forces in containing the Taliban insurgency since most North Atlantic Treaty Organisation troops left in 2014, leaving a smaller training and advisory mission.
The defence ministry says 135 recruits were killed and 64 wounded in the raid.
Followers were told they can be "suicide attacks, complex attacks and inside attacks" by soldiers or police turning against their peers. In an emailed statement the Taliban also claimed the district, while Badakhshan's deputy governor Mohammad Bidar said fighting between Afghan Security Forces and the Taliban was still intense in the area.
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The Taliban's annual spring offensive normally marks the start of the "fighting season", but this year militants continued fighting during the winter months.
In his statement, Mujahid boasted Taliban control over more than half of the country, referencing to a February report issued by Washington's special inspector general for Afghan reconstruction. They are largely conducting a training, advise and assist mission aimed at supporting Afghan forces.
The attackers carried valid passes to the base, security sources said, and were dressed in Afghan army uniforms.
It was the first time the U.S. military's GBU-43/B Massive Ordnance Air Blast, dubbed the "Mother of All Bombs" had been used in combat.
The attack occurred in the same area where two weeks ago the USA dropped its largest non-nuclear bomb on an IS complex.
The troops were working with partnered Afghan soldiers in the raid against ISIS Khorasan, a local offshoot of the jihadist group based in Iraq and Syria.
Some analysts even argued the strike could boost the Taleban, who had been fighting a turf war with ISIS in Nangarhar province near the border with Pakistan, where the bomb was dropped.
The bombing triggered global shockwaves, but was criticised by observers who questioned its use against a group that is not considered as big a threat as the Taliban.