Improving Job Opportunities for Veterans Act of 2013 - Directs the Secretary of Veterans Affairs (VA), for a certain four-year period, to require training establishments applying for state approval of on-the-job training programs to certify that the wages to be paid an eligible veteran or person upon entrance into training will be increased in regular periodic increments until, by the last full month of the training period, they will be at least 75% (currently 85%) of the wages paid for the job for which such eligible veteran or person is being trained.

Requires the Secretary to enter into agreements with the heads of other federal departments and agencies to operate similar on-the-job training programs to train eligible veterans or persons to perform skills necessary for employment by the department or agency operating the program.

Extends from November 30 through December 31, 2016, the requirement of a reduced pension ($90 per month) for veterans (with neither spouse nor child) or surviving spouses (with no child) covered by Medicaid plans under title XIX of the Social Security Act for services furnished by nursing facilities.