A US team writing in the New England Journal of Medicine say Down's syndrome can now be reliably tested for in the mother's blood.
Meanwhile, Great Ormond Street Hospital has started offering similar tests. A decision on whether the UK's Down's syndrome screening programme should change is due this year.
At the moment in the UK, a woman is assessed based on her age and an ultrasound scan, with those deemed high-risk having further tests.
These involve a needle taking a sample of the placenta or the fluid that bathes the baby. There is a risk of miscarriage with the procedure.
Blood tests look for fragments of DNA from the placenta, which drift about in the mother's bloodstream.
Down's syndrome is caused by an extra copy of a huge stretch of DNA and that extra bundle of genetic information can be detected in the blood.
If initial tests are more accurate they could reduce the number of women who go on to have the invasive test.
Previous research had suggested the tests were effective in high-risk women.
Now a team at the University of California, San Francisco, suggests the blood test could replace current tests for all women.
They correctly identified 38 cases of Down's syndrome out of nearly 16,000 women tested. The basic risk screening found only 30 cases and had a higher rate of false-positives.
The UK's national screening committee will assess the new tests in June.
Professor Lyn Chitty, from Great Ormond Street, has been evaluating how they could be introduced across the NHS.
She says testing every pregnant woman's blood is unlikely. However, she says it can and should be integrated into the existing screening so that high-risk women have an extra check before deciding if an invasive procedure is needed.
She told the BBC: "These are really exciting times; this cell-free DNA is changing prenatal care dramatically.
"I think it broadens access to testing. really; a number of women will decline invasive testing because of the risk of miscarriage and they may well take up non-invasive prenatal testing."
She said progress in the area was "very rapid" and tests for other genetic disorders such as cystic fibrosis were also becoming available.
Great Ormond Street already has an approved test which it has started offering in parts of London.
The Down's Syndrome Association said that if the changes did come into force then the risks and benefits need to be clearly communicated to parents.
"At the time of testing, easily understood and up-to-date information must be provided in an unbiased way by well trained professionals," the organisation said in a statement.