Unemployed veterans who were discharged honorably on or after July 1, 1981, may be eligible for 13 weeks of unemployment insurance benefits under a new federal law.

The law, signed last month by President Reagan, modifies 1981 amendments to the Unemployment Compensation Act for ex-military personnel that disqualified those who voluntarily left the military service or who were separated for just cause. Veterans were considered to have left the military service voluntarily if they had the option to reenlist but chose not to.

The new unemployment insurance eligibility rules require veterans to have completed the first full term of active service they initially agreed to serve, and those who were separated to have been separated under honorable conditions. Some who left the service before their first term was completed also are eligible.

Veterans who filed unemployment claims between Aug. 16, 1981, and Oct. 29, 1982, and were denied benefits under the old provisions may qualify under the new law.

When filing a claim, persons should bring Form DD-214, the Certificate of Release of Discharge From Active Military Service, to any of the city's five unemployment services centers: 1000 H St. NW; 1319 H St. NE; 4120 Kansas Ave. NW; 1217 Good Hope Rd. SE, or Eighth and Xenia streets SE.