Human Cloning Prohibition Act of 1998 - Amends the Federal criminal code to prohibit any person or entity: (1) in or affecting interstate commerce, from using human somatic cell nuclear transfer technology; and (2) from importing an embryo produced through such technology.

Sets penalties for violations of this Act of: (1) up to ten years in prison, a fine, or both; and (2) not more than twice the amount of any gross pecuniary gain derived from such violation.

Establishes within the Institute of Medicine the National Commission to Promote a National Dialogue on Bioethics. Directs the Commission to provide an independent forum for broad public participation and discourse concerning important bioethical issues, including cloning. Sets forth reporting requirements. Authorizes appropriations.

Expresses the sense of the Congress that the Federal Government should advocate and join an international effort to prohibit the use of human somatic cell nuclear transfer technology to produce a human embryo.