Claims asserted and compensable but unsatisfied under provisions of section
1321 of title
33, which are modified by section 304 of this Act may be asserted against the Fund under this subchapter; and other claims resulting from a release or threat of release of a hazardous substance from a vessel or a facility may be asserted against the Fund under this subchapter for injury to, or destruction or loss of, natural resources, including cost for damage assessment: Provided, however, That any such claim may be asserted only by the President, as trustee, for natural resources over which the United States has sovereign rights, or natural resources within the territory or the fishery conservation zone of the United States to the extent they are managed or protected by the United States, or by any State for natural resources within the boundary of that State belonging to, managed by, controlled by, or appertaining to the State, or by any Indian tribe or by the United States acting on behalf of any Indian tribe for natural resources belonging to, managed by, controlled by, or appertaining to such tribe, or held in trust for the benefit of such tribe, or belonging to a member of such tribe if such resources are subject to a trust restriction on alienation.