Researchers may finally be closing in on a way to screen healthy women for ovarian cancer — a disease that rarely shows symptoms until it’s too late to cure.

A simple blood test followed by ultrasound exams as needed found deadly tumors before they caused symptoms, and without giving too many false alarms, doctors reported Thursday.

The study, in more than 3,000 American women, is not big enough to justify screening with this method now. But doctors are encouraged because it confirms early results from a much larger study under way in England that will give a clear answer in a few years.

More important, the U.S. study suggests that this approach can find aggressive tumors — the ones that threaten lives — without putting many healthy women through unnecessary follow-up tests. Very few women needed exploratory surgery after screening, and of those who did, one in three turned out to have an invasive cancer.

The method “is starting to look very, very promising,” said the study’s leader, Dr. Karen Lu of the University of Texas M.D. Anderson Cancer Center in Houston. She gave results Thursday in a telephone briefing and will present them next month at an American Society of Clinical Oncology conference.

Ovarian cancer is so deadly because nearly 80 percent of cases are found at an advanced stage. About 21,550 women were diagnosed with it, and 14,600 died in the U.S. last year.