The Department of Veterans Affairs would get $64 billion in discretionary spending under President Obama’s fiscal 2013 budget proposal, a 4.5 percent rise that includes an 18 percent increase in medical care for the growing number of veterans returning from Iraq and Afghanistan.

The VA’s mandatory budget, which is mostly for disability compensation and pensions, would jump to $76.3 billion, a 16.2 percent increase, fueled by claims related to Vietnam War-era Agent Orange exposure, and Obama’s proposal to create a $1 billion Veterans Job Corps putting veterans to work on federal lands. Overall, the VA budget would reach $140.3 billion, an increase of 10.5 percent.

One of the biggest proposed increases in discretionary spending seeks to build on progress toward a high-profile goal: eliminating veteran homelessness by 2015.

The proposed budget is aimed at “taking the next step in ending veterans homelessness,” VA Secretary Eric K. Shinseki told reporters at a budget briefing Monday afternoon.

The proposed budget includes $1.35 billion for programs on homelessness, an increase of 33 percent, or $333 million, from 2012.

Included are $200 million to provide grants and technical assistance to community nonprofit groups that help at-risk veterans keep their homes or get them rapidly into new housing, and $43 million for housing vouchers for homeless veterans.

An additional $21 million would create positions for 200 coordinators who would help homeless veterans with disability claims, housing problems, job and vocational opportunities, and problems with the courts.

The latest figures show that the number of veterans homeless on a given night dropped from 76,300 in 2010 to 67,500 in 2011. The VA projects the budget increase will drop the numbers to 35,000 by the end of fiscal year 2013.