Fiscally Responsible Israel Security Supplemental Appropriations Act, 2024 This bill provides FY2024 supplemental appropriations to the Department of Defense (DOD) and the Department of State for activities to respond to the attacks in Israel. The bill designates the funding as emergency spending, which is exempt from discretionary spending limits. Specifically, the bill provides appropriations to DOD for Military Personnel; Operation and Maintenance; Procurement; Research, Development, Test and Evaluation; Defense Working Capital Funds; and the Defense Health Program. The funding is provided for purposes such as supporting current U.S. military operations in the region; replacing defense articles that were provided to Israel; reimbursing DOD for defense services and training provided to Israel; and procuring Israel's Iron Dome, David's Sling, and Iron Beam defense systems to counter short-range rocket threats. The bill also provides appropriations to the State Department for Diplomatic Programs, Emergencies in the Diplomatic and Consular Service, and the Foreign Military Financing Program. The funding is provided to the State Department for purposes such as (1) increasing security at U.S. embassies impacted by the attacks on Israel, and (2) conducting emergency evacuations of U.S. government personnel and citizens in the region. In addition, the bill includes provisions that expand the authorities of the President to transfer defense articles and services from DOD to Israel. Finally, the bill rescinds specified unobligated funds that were provided for the Department of Commerce Nonrecurring Expenses Fund by the Fiscal Responsibility Act of 2023.