The bipartisan measure has 26 co-sponsors and a companion bill in the House with 53.
The bill provides for payments to employers for on-the-job training, creates new direct federal hiring authority so that more service members have jobs waiting for them when they leave the military and improves veteran mentorship programs.
The unemployment rate for veterans returning from Iraq and Afghanistan has hovered around 11 percent. The jobless rate for veterans between the ages of 20 and 24 has been as high as 27 percent.
"I’m hopeful that this legislation will quickly make its way before the full Senate, and I look forward to fighting for it when it does,” Murray said
The jointly sponsored bill would modify federal hiring practices to encourage hiring veterans and to begin the process before leaving the service.
The bill also would require mandatory participation in the Transition Assistance Program and require the Labor Department to meet with veterans to determine their employment status and if they need assistance.
In addition, the measure continues a program that provides rehabilitation and vocational benefits to severely wounded service members, provides up to an additional 24 months of vocational rehabilitation and employment services to veterans who have exhausted these and state-provided unemployment benefits and requires the Veterans Affairs Department to meet periodically with veterans who have participated in its vocational rehabilitation program to determine employment status.