President Donald Trump’s first budget proposal would offset a roughly $20 billion boost in military spending from current levels by cutting funding across the rest of the government, including international aid programs, the White House said Monday.

The increase would translate to a funding boost of nearly 2% from current levels, which defense hawks in Congress said Monday was insufficient. But compared to budget caps in place for 2018—part of across-the-board spending cuts established in 2011—Mr. Trump’s budget proposal calls...