The District of Columbia has the unwelcome distinction of having the nation's highest cancer death rate, but a woman's anonymous bequest is helping to combat this grim fact by offering an attractive bargain: free health testing.

Since Jan. 31, when the local chapter of the American Cancer Society announced that the woman's $500,000 gift would be used to give free cancer tests to any District resident, telephone lines to the three screening sites have been jammed.

More than 1,500 people have called to seek appointments under special screening programs at Providence Hospital, the Washington Hospital Center and the Howard University Cancer Center.

Providence, which added extra nurses and nurse practitioners to handle the load, now has a one-week wait for appointments. At the Hospital Center, the next open appointment is July 15. And Howard, which has screened 230 people, is scheduling visits for late September.

"We have been so pleased with the response, but there's no question it's been frustrating for many people trying to get through," said Lois Callahan, a cancer society spokeswoman. "We want to assure everyone they will get an appointment and they should keep trying."

Those who live near one of the three hospitals are being encouraged to set up appointments in person, she said. She advised others to telephone early in the day.

The program has been expanded to city-run health clinics, which will run the same full range of cancer screening tests on patients who request it. The test materials are being donated by the society under the bequest program, Callahan said.

The exams take about 40 minutes and are aimed at detecting cancer early, when many treatments are successful.

The tests could cost as much as $200 in a private doctor's office. Although the program is aimed at District residents, no one will be turned away, officials said, adding that non-District residents will be asked to make a donation.

Those interested in making an appointment can call Providence Hospital at 269-7986, Washington Hospital Center at 541-6710, or Howard University Cancer Center at 636-7610.