A bench of Chief Justice D N Patel and Justice Prateek Jalan issued notice to the Delhi government and the All India Institute of Medical Sciences (AIIMS) seeking their stand on the woman's plea.
The court asked the woman to approach the AIIMS for setting up a panel of experts to examine her and asked the institute to evaluate her and the foetus to ascertain whether it would be safe to terminate the pregnancy.
The bench asked the AIIMS to give its report by July 13 after examining the woman and listed the matter for hearing on July 14.
The woman, in her plea filed through advocate Sneha Mukherjee, has said the foetus suffers from "spina bifida and Arnold Chiari Syndrome defect" which results in the spinal cord being outside the body and the brain tissue extending into the spinal canal.
The foetus also suffers from a deformed skull and a heart defect according to ultrasound reports, the petition has said and added that these abnormalities would make it improbable for the baby to survive after birth.
If the pregnancy is allowed to continue, it could also cause irreparable physical and psychological damage or trauma to the woman, the plea has said. HMP SKV DV DV