Whatever they agree upon then goes to the Afghan parliament, which could make still more changes before the agreement is approved.
The Jirga will hold a series of closed-door meetings until Sunday, when it makes its suggestions on the security deal to Karzai.
On the U.S. side, only the administration of President Barack Obama needs to approve the agreement, but it could reject changes made by Afghan officials.
If it does, that leaves open the option for the U.S. to pull all troops out of Afghanistan.