Robert L. Ashworth, 60, director of the National Veterans Service of the Veterans of Foreign Wars, died Thursday at Parklawn Memorial Hospital in Dallas, following a heart attack. He had been in Dallas to attend the VFW's 79th national convention.

Mr. Ashworth, who served in the Army in World War II and was wounded in North Africa began in career as a VWF official in 1944 here. He was a service officer here, representing veterans and their families seeking claims from the Veterans Administration and othe agencies. That is the function of the National Veterans Service and Mr. Ashworth remained in that work for the rest of his life.

He served as a claims officer in Philadelphia from 1945 to 1950, and then returned to Washington. He was a claims consultant here from 1951 to 1963, when he became assistant director of the National Veterans Service.

In 1974, he was made director of the service.

Mr. Ashworth was born in Calgary, Alberta, and grew up in Pittsburgh. He joined the Army after completing Mount Saint Mary's High School there. He was discharged because of his wounds and then joined the VFW. He attended the old National Law School here.

He was a member of VFW Post 344 in Williamsport, Pa.

Survivors include his wife, Sandria, of the home in New Carrollton; three children, Robert L. Jr., of Laurel, Joe C., of Silver Spring, and Debra L., of Lanham, and five stepchildren, Stephanie Schatzer, of Seattle, William Neville, of Morgantown, W. Va., and Joseph J. Gerstle III, John David Gerstle and Debra Anne Gerstle, all of the home.

The family suggests that expressions of sympathy be in the form of contributions to the American Heart Fund, or to the Memorial Fund of Riverdale Presbyterian Church, University Park, Md.