"The Islamic Emirate will provide safety to anybody who defects from the Kabul puppet regime," the Taliban said in a statement on their website today, using their formal name.
"They can get in touch with us 24/7 through these phone numbers and email addresses," it added, listing two for each.
The move demonstrates the Taliban's efforts to boost public support for their resilient but unpopular insurgency following a string of defections to the Islamic State group in recent months.
When AFP called one of the numbers, a militant representative who identified himself as Mullah Jalid said they had received more than 20 calls from government employees since the statement was posted.
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"They all said labayk (Arabic for 'we are at your service') to our invitation," Jalid said, a claim that was impossible to verify independently.
"This invitation is for all the employees of the government, military and civilian. They are welcome to come to us and we will protect them from the invaders and the stooge government."
Once seen as uneducated thugs, the Taliban have developed a media-savvy PR team who use digital technology to reach out to audiences worldwide.
When the Taliban ruled Afghanistan between 1996 and 2001, almost all electronic products were outlawed as un-Islamic.
Photographs of living things were illegal and ownership of a video player could lead to a public lashing.
But the Taliban have avidly embraced electronic communication and social media in recent years as a recruitment tool and to promote their propaganda.
The Taliban are seeking to halt defections to the Islamic State after some insurgents adopted the IS flag to rebrand themselves as a more lethal force as NATO troops depart.
Last Tuesday the Taliban warned the leader of the Islamic State group against waging a parallel insurgency in Afghanistan, after reported clashes with militants loyal to IS.