International Assistance to Missing and Exploited Children Act of 2004

International Assistance to Missing and Exploited Children Act of 2004 - Amends the International Child Abduction Remedies Act (ICARA) to make Federal Tort Claims Act provisions applicable to the National Center for Missing and Exploited Children (Center) and other entities to which responsibilities are delegated under ICARA by the U.S. Central Authority under the Hague Convention on the Civil Aspects of International Child Abduction.

Amends the Federal judicial code to authorize actions in U.S. district court to resolve conflicting child custody determinations.

Directs the Attorney General to establish a registry of custody and visitation orders and proceedings. Provides guidelines for disclosing registry information.

Authorizes law enforcement officials to detain children listed as missing or accompanying an adult arrested for suspected child abduction in violation of a custody order. Requires officials to surrender such children to the appropriate State agency as soon as practicable.

Requires the Central Authority to: (1) fund legal services to persons seeking remedies in parental kidnapping cases; (2) provide related training and technical assistance; and (3) encourage the designation of courts to hear Convention-related cases.

Requires the Federal Judicial Center to provide continuing education on the Convention and related laws.

Requires annual reports to Congress on: (1) progress in negotiating international child abduction agreements with countries that are not parties to the Convention; and (2) cases involving extradition requests of individuals alleged to have violated international parental kidnapping provisions.

Requires the Attorney General to support State adoption and implementation of the Uniform Child Custody Jurisdiction and Enforcement Act.

Amends the Violence Against Women Act of 2000 to include children at risk of parental kidnapping in the Safe Havens for Children Pilot Program.

Amends the Internal Revenue Code of 1986 to authorize disclosure of taxpayer identity information to the Center.

Calls for increasing the U.S. contribution to the Permanent Bureau at The Hague.