The offensive, dubbed "Operation Omari", began at 5:00 a.m. (local time) the outfit said in the statement, Xinhua news agency reported.
"Operation Omari began across Afghanistan at 5 a.m. We pray to Allah Almighty that he blesses our Operation Omari in a similar fashion and ordain it with great Islamic victories on the battlefield and the unconditional defeat and withdrawal of the foreign invaders and their internal servants," the statement said.
Militancy and conflicts typically gain momentum in spring and summer in Afghanistan, commonly known as fighting season among Afghans.
In the statement, Taliban militants also called upon Afghan civil and military servicemen to desert government rank and join "Islamic Emirate of Afghanistan" (name of Taliban ousted regime) which had ruled major part of the country before its collapse in late 2001.
"With the advent of spring, it is again time for us to renew our Jihadi determination and operations," the statement said.
The US and NATO-led troops ended their combat mission in Afghanistan in December 2014, facilitating Afghan national security force to shoulder alone the security responsibilities of their conflict-ridden country from January 1 last year.
However, some 13,000 foreign forces are currently stationed in the militancy-hit Afghanistan within the framework of the NATO-led Resolute Support (RS) mission to help Afghan forces in the field of training and advising.(IANS)