The conventional methods involve tests such as amniocentesis, in which a sample of amniotic fluid surrounding the fetus is taken; however, it increases the risk of suffering a miscarriage.
The researchers said that the blood of a pregnant woman contains DNA from both herself and from her fetus. This genetic material can be removed from a blood sample and screened for disease genes.
It may be possible to detect errors in a single gene by taking blood from the mother and counting the ratio of mutations to normal genes.
With the help of a technique called digital polymerase chain reaction, (dPCR), the researchers were able to count copies of the gene for beta-thalassaemia in blood samples from pregnant women.
By noting ratios of recessive genes relative to normal copies of the gene, the researchers were able to work out if the fetus would develop the disease.
"We believe that the large proportion of invasive prenatal tests will one day be replaced," New Scientist quoted Lead researcher Dennis Lo of the Chinese University of Hong Kong, as saying.
"This [new] test saves those babies who would be incidentally aborted by invasive testing," he added.
The study appears in Proceedings of the National Academies of Science.