The bill, proposed by Welfare Minister Yitzchak Herzog, deliberately excludes terrorists from funeral coverage.
A similar bill was proposed during the last Knesset session by MK Gidon Saar of the Likud. The bill won initial Knesset approval.
Saar wrote his version of the bill after realizing that the family of a terrorist from east Jerusalem who had used a bulldozer to attack Israeli motorists and passersby, murdering three, could require the NII to cover his funeral costs.
Herzog's bill joins a number of other legislative reforms that have gradually stripped terrorists' families of the benefits normally granted to survivors following a death.
The families of terrorists with Israeli citizenship or Jerusalem resident status are not eligible for the payments usually given to orphans, widows, and others who have lost a loved one.
"A person who chose to end innocent lives, and to carry out acts of terrorism against the state of Israel and its citizens, has no right to come and make claims,” Herzog said in explanation of his bill.