The team from the University of Washington used pieces of the fetus' DNA that were in the pregnant woman's blood.
These were used along with the parents' DNA to build a complete 'map' of the fetus' genome.
They compared the genetic map drawn 18 weeks into pregnancy with DNA taken from the umbilical cord after birth and it was 98% accurate.
The scientists hope the development will eventually lead to fetuses being screened for thousands of genetic disorders in a single test.
One of the researchers, Dr Jay Shendure, said: ‘This work opens up the possibility that we will be able to scan the whole genome of the fetus for more than 3000 single-gene disorders through a single, non-invasive test.’
They say genetic defects which are not present in the parents could be picked up too, if it is possible to improve the technique.
However, the team has stressed that they expect their research to raise ethical questions.
And pro-life groups have been critical of the work because they believe it will lead to more abortions.
The findings of the research are published in the journal Science Translational Medicine
To read the abstract, please click here