The newspaper said the re-vetting process will affect more than 27,000 Afghan troops.
The suspension comes in response to the killing of at least 45 foreign troops this year by their Afghan colleagues.
“We have a very good vetting process,” the paper quotes an unnamed senior special operations official as saying. “What we learned is that you just can’t take it for granted. We probably should have had a mechanism to follow up with recruits from the beginning.”
According to The Post, numerous military guidelines were not followed by either Afghans or Americans because of concerns that they might slow the growth of the Afghan army and police.
Nato has some 130,000 troops in Afghanistan fighting the Taliban’s decade-long insurgency alongside government forces.
Most of the Nato troops are set to withdraw by the end of 2014 in a US-designed transition process that will put Afghan security forces in charge of security for their war-battered country.
The process is already under way, with security responsibilities of about half of the Afghan population transferred to the local security forces.
The Taliban have stepped up their attacks in recent months as part of efforts by the insurgency to undermine the transition process.