WASHINGTON—Senate Republicans issued a five-year budget plan Friday that calls for reducing the federal deficit and diverges from the White House over how much to stash in an emergency war fund.

The budget resolution aims to cut mandatory spending, the part of federal funding extended on auto-pilot, by $551 billion by 2024. Republicans have long targeted this chunk of the federal budget, which pays for programs including Medicare and Medicaid, as the best opportunity for reining in spending. Mandatory spending makes up more...