The bodies were found in a psychiatric ward at the weekend in the southern town of Pau. One had been beheaded while the other had her throat slit.
Police have released an ex-patient held for questioning, the sixth suspect detained and freed since the deaths.
Mr Chirac said whoever was behind the “savage murders” would be punished.
“We need better co-ordination, better support of the [mentally] ill and improved security in hospitals. This is a major imperative,” he was said through a spokesperson.
Hospitals in France have observed a minute’s silence in memory of Chantal Klimaszewski, 48, and Lucette Gariod, 40, whose bodies were found on Saturday.
Staff turning up for the day shift found evidence of a break-in and a 20-metre long trail of blood.
The head of one of the nurses had been placed on top of a television set.
Police released without charge a former patient at the institution who was arrested in the south-western town of Saint-Jean-de-Luz.
Five other people, one of them also a former patient, were detained on Saturday before being released.
Staff held a vigil outside the hospital in memory of their colleagues.
Some demanded that the unit where the murders took place be closed.
Health Minister Philippe Douste-Blazy says new security measures will be implemented within the next few weeks.
He said full details of the new measures, will be announced in February after a judicial enquiry.
One of the proposals under consideration includes installing an alarm system from psychiatric hospitals and emergency wards to local police stations.Categories : 上海性息网