But the group warned its fighters would "strongly defend" themselves if attacked, according to a statement sent to the media two days after the Afghan government announced a week-long ceasefire.
"All the mujahideen are directed to stop offensive operations against Afghan forces for the first three days of Eid-al-Fitr," the Taliban said in a WhatsApp message.
"But if the mujahideen are attacked we will strongly defend (ourselves)." The Taliban added that "foreign occupiers are the exception" to the order sent to its fighters.
The announcement came after President Ashraf Ghani on Thursday declared an apparently unilateral week-long ceasefire with the Taliban.
It would last "from the 27th of Ramadan until the fifth day of Eid-al-Fitr", Ghani tweeted from an official account, indicating it could run from June 12-19.