But the provisions have angered minority groups in Israel, with members of the Druze community expected to mount a legal challenge.
Mr Kahlon said the Druze concerns demonstrated the law had been "passed in haste."
"The last thing that we want is to harm the Druze community," he told Israeli army radio.

Mr Bennett had earlier said the Druze were "our brothers who stand shoulder to shoulder with us on the battlefield".
"We, the government of Israel, have a responsibility to find a way to heal the rift," he said.