DNA samples from the four couples will now be compared with biological samples from the two fetuses.
The decision to carry out the DNA testing was made following a long meeting between the management of the ASL (the local health authority), the regional commission and inspectors from the Ministry of Health, Il Messaggero reported.
On Sunday, Italy’s Health Ministry said it was launching an investigation into the embryo mix-up, which was only discovered after the woman was three months pregnant with the twins.
The investigation is being led by geneticist Giuseppe Novelli and will look into whether there was any further mix-up of the embryos of two of the other women.
The mistake happened on December 4th, when four different couples were receiving treatment at a specialist fertility unit at the Sandro Pertini Hospital in Rome.
It is not clear whether the mistake led to any of the other women becoming pregnant with the wrong baby.
Health Minister Beatrice Lorenzin said on Sunday investigators would look at whether the hospital had "respected all the legal procedures" and expressed concern that she had only learnt about the mistake through press reports.
"The national standards on assisted fertilization, which are based on European directives, are very rigorous, and if applied correctly, guarantee the traceability of all biological material used in the reproduction process," she said.
The local health authority in Rome said it only became aware there was a problem of "genetic incompatibility" between the parents and the embryos on March 27th.
It said it has halted all embryo implantations at the clinic until further notice.
Of the four women given fertility treatment on December 4th, one of them did not fall pregnant, Il Messaggero reported on Tuesday.
In an interview with the paper, the 36-year-old woman – who has not been named – said that if the babies turned out to be hers then she would want to keep them.
Recalling the moment she found out about the mix-up, the woman said: “Oh my God, those babies could be mine.”
“I don’t want to be confused for a crazy person who is not able to have children and so wants those of other people,” she said.
“I just want everything to be clear. I want to know if the embryos in the mix-up are mine or not. If they are mine, obviously they are mine and my husband’s babies.”