Foreign Relations Authorization Act, Fiscal Years 2004 and 2005

Foreign Relations Authorization Act, Fiscal Years 2004 and 2005 - Authorizes appropriations to the Department of State for FY 2004 and 2005 for the administration of foreign affairs, international organizations and conferences, certain international commissions, migration and refugee assistance, and specified centers and foundations.

Amends Federal law to. provide for: (1) grant authority to promote biotechnology; (2) immediate response facilities under the Secure Embassy Construction and Counterterrorism Act of 1999; (3) mine action programs grant authority; (4) a U.S. Diplomacy Center; and (5) public affairs grant authority.

Amends Federal civil service law and the Foreign Service Act of 1980 to provide for: (1) cost of living allowances for State Department personnel; (2) a waiver of annuity limitations on re-employed foreign service annuitants; (3) a Fellowship of Hope Program; (4) claims for lost pay; (5) suspension or enforced leave of Foreign Service members; and (6) an Ombudsman for the Department of State.

Amends the Foreign Service Act of 1980 to repeal the recertification requirement for Senior Foreign Service.

Amends the Foreign Relations Authorization Act, Fiscal Years 1994 and 1995 to raise the cap on peacekeeping contributions.

Amends the Immigration and Nationality Act to revise requirements for designation of foreign terrorist organizations.

Amends the Foreign Relations Authorization Act, Fiscal Year 2003 to allow the use of Economic Support Funds to address the water needs of Southern Lebanon.

Amends the Arms Export Control Act to: (1) raise the minimum thresholds for congressional notification of specified arms transfers; (2) authorize the President to waive any requirements for a bilateral agreement relating to licensing of defense exports; and (3) authorize appropriations for foreign military financing, international military education and training (IMET), and nonproliferation, anti-terrorism, demining, and related programs.

Provides for presidential authority to waive restrictions and eligibility requirements under the Cooperative Threat Reduction Act of 1993 with respect to an independent state of the former Soviet Union for a fiscal year.

Amends the Arms Export Control Act to: (1) require congressional notification for comprehensive defense export authorizations; and (2) revise authorities for loan of material, supplies, and equipment for research and development purposes.

Authorizes the transfer of certain obsolete or surplus defense articles in the war reserve stockpiles for allies to Israel.

Extends certain waivers with respect to assistance to Pakistan.

International Parental Child Abduction Prevention Act of 2003 - Amends the Immigration and Nationality Act to revise requirements with respect to the inadmissibility of aliens supporting international child abductors and relatives of such abductors.

Repeals specified reporting requirements.

Amends the Arms Export Control Act to repeal the requirement for annual renewals of presidential nuclear reprocessing transfer waivers.

Establishes a United States Complex Foreign Contingency Fund from which the President is authorized to furnish on such terms and conditions as he may determine assistance to respond to complex foreign: (1) political crises threatening democratic institutions; (2) food, agricultural or health crises; or (3) fiscal or economic crises affecting countries, regions or ethnic groups.