National Whale Conservation Fund Act of 1998 - Amends the National Fish and Wildlife Establishment Act to authorize the National Fish and Wildlife Foundation to establish a national whale conservation endowment fund to be used to support research, management activities, or educational programs that contribute to the protection, conservation, or recovery of whale populations in U.S. waters.

Permits the Foundation to enter into appropriate arrangements to provide for the design, copyright, production, marketing, or licensing of logos, seals, decals, stamps, or any other item that the Foundation determines to be appropriate to raise funds to be deposited in the fund.

Authorizes the Secretary of Commerce to transfer to the Foundation for deposit in the fund: (1) any amount received by the Secretary as a civil penalty assessed under the Marine Mammal Protection Act of 1972; or (2) any amount received by the Secretary as a settlement or award for damages in a civil action or other legal proceeding relating to damage of natural resources.

Declares it is the intent of the Congress that, in making expenditures from the fund, the Foundation should give priority to projects that address the conservation of populations of whales that the Foundation determines: (1) are the most endangered; or (2) most warrant, and are most likely to benefit from, research management or educational activities.

Requires the Directors to consult with the Administrator of the National Oceanic and Atmospheric Administration and the Marine Mammal Commission in carrying out any action under this Act.