make grants to or contracts with Federal and other public departments or agencies, and private nonprofit organizations, for the assignment or referral of volunteers under the provisions of title I of the Domestic Volunteer Service Act of 1973 [
42 U.S.C. 4951 et seq.] (except as provided in section 108 of such Act [
42 U.S.C. 4958]), which may provide that the agency or organization shall pay all or a part of the costs of the program; and