Pregnant women are offered a number of tests
Tests used in pregnancy only pick up half of potential chromosomal abnormalities, Italian research warns.
The team behind the work told a European genetics conference that women needed more information about their limitations, and the risks involved.
Some tests which sample the fluid around the foetus can cause miscarriage.
The Royal College of Midwives said that the UK focused on a small number of common defects, with high quality
information for women.
Perhaps the best known example of a chromosomal abnormality is Down's syndrome, in which the foetus has an extra copy of one of the chromosomes.
It leads to babies who have development problems, a higher rate of cardiac defects and a characteristic facial appearance, although with the support of modern medicine, people with Down's can live in excess of 50 years.
One way to confirm the syndrome is via amniocentesis, in which a needle is used to take a sample of the fluid within the womb.
This test, which is not routinely offered to all pregnant women in the UK, can also reveal other, less common, chromosomal defects, such as Edward's syndrome and Patau syndrome.
Approximately one in 100 women who have the test will miscarry as a result.
Dr Francesca Grati, from the TOMA Laboratory in Busto Arsizio, looked at well over 100,000 prenatal diagnoses which used invasive tests such as amniocentesis, and looked to see which chromosomal abnormalities had been missed in the samples.
Addressing the European Society of Human Genetics conference in Barcelona, she said that the tests had only identified half the abnormalities present in the samples. "There are many others which are not picked up by these tests, and the tests do not even detect 100% of the common abnormalities."
She said it was "fundamental" that doctors should counsel their patients about the limitations of current screening methods, so that they could make an informed choice about the risks invasive tests such as amniocentesis.
However, a spokesman for the Royal College of Midwives said that it was right to focus testing on a small number of the most common defects, rather than bombard women with worrying information about very rare conditions.
She said: "I think we are very good at providing information to women in this country about these tests and their risks.
"If you were to tell women about 50 different conditions, some of which have a one in 150,000 chance of happening, they will not be able to absorb it."