Activists and Western governments had sought to derail the legislation, which would have prevented victims from testifying about domestic violence, child abuse or forced marriage, the British newspaper the Guardian reported.
The legislation became public last month and spokeswoman Adela Raz said the Cabinet ordered changes in a section of the law Monday. She said Karzai decided the section "needs to be amended," but she did not say how the bill would be altered.
Conservative lawmakers have previously blocked efforts to change the bill.
The law does not define who is a relative, so it could cover many people in villages with a great deal of intermarriage between families.