Taliban spokesman Zabiullah Mujahid said on Friday that the militants fired two missiles into the US airbase in Bagram in the early hours of the day.
He said many American forces were killed in the assault.
US military officials confirmed the airbase was attacked, but gave no further details as on the number of possible casualties.
The Bagram airbase, the largest US military base in Afghanistan, is located in Parwan Province, north of Kabul.
On Wednesday, Panetta reportedly escaped a suspected car bomb attack after a man drove a stolen vehicle onto the runway where his plane was to land, in Camp Bastion military base in Afghanistan.
Panetta’s visit came days after US forces went on a shooting spree which killed more than 16 Afghan civilians inside their homes in southern province of Kandahar.
In late February, US troops in the base sparked outrage among Afghans after they burned copies of the Holy Qur’an seized from the inmates held in Bagram’s US-run detention center.
The move triggered protests across Afghanistan, where dozens of people including several US forces were killed.
The base, frequently targeted by Taliban rocket and mortar rounds, has witnessed a rise in the attacks.
On March 10, the Taliban claimed responsibility for an attack on the US base, claiming that a number of foreign soldiers were killed in the assault.
The attack came after the United States finally agreed to hand over control of the notorious Bagram prison to Afghan authorities, in a move to reduce strains in Kabul-Washington ties.
AZA/MRS/JR/HGH
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