WASHINGTON—President Biden on Monday released a $5.8 trillion budget that envisions a substantial increase in U.S. defense spending, a sign of the administration’s willingness to devote additional resources to military programs, including aiding Ukraine in its fight against Russian aggression.

The Biden administration is seeking $813 billion for military spending in fiscal year 2023, which begins Oct. 1, a roughly 4% increase from the $782 billion enacted for this fiscal year.