WASHINGTON (AP) _ Sen. Jake Garn, who gave one of his kidneys to his daughter, said today they will launch an effort to encourage Americans to donate their organs after death.

''There are tens of thousands of people out there dying, waiting for hearts, waiting for kidneys, waiting for corneas. So, Sue and I are both going to work at encouraging people to be donors, to give the gift of life after they've gone,'' Garn, R-Utah, said in an interview on NBC-TV's ''Today'' show.

Garn, 53, and his daughter, Susan Garn Horne, 27, were interviewed by three network news shows today, Garn from Salt Lake City and Mrs. Horne from McLean, Va.

Doctors at Georgetown University Hospital in Washington removed Garn's kidney Sept. 10 and transplanted it into Mrs. Horne, whoe own kidneys were failing because of diabetes.

Garn said he and his two sons, ages 20 and 28, were nearly identical matches to his daughter and all would have made good donors. But, he said on ABC-TV's ''Good Morning America'' that he decided to donate his kidney because ''it seemed to me it made sense. ... I didn't need a kidney nearly as long as my two sons.''

''If Sue did at some time in the future reject this particular kidney, then she's got two brothers who are backups and were perfectly willing to donate their kidneys, so we thought it was a little bit of an insurance policy,'' he said.

''I was lucky,'' Mrs. Horne told the CBS ''Morning News''. ''I had a living related donor and I had backups to use, but a lot of people don't have that luxury, and so if people would be more willing to donate their organs, it would really be a big help.''

Both Mrs. Horne and Garn said they felt good, Garn adding that he expected to be back to work by next week.

''It's just the most satisfying thing a father could witness to see one of his children improve so dramatically. It's just a very special feeling knowing that part of me is inside her,'' Garn told CBS. ''We feel very blessed. It's gone just like the medical text books say it should go so far.''

Said Mrs. Horne, on ABC: ''It's an incredible feeling and almost an unbelievable one to imagine that I actually have my father's kidney inside me and it's working very well, doing its job.''