The boys are in "truly remarkable condition, considering their ordeal," James Thomas, chief of critical care services at the Children's Medical Centre in the Texan city of Dallas, told reporters on Monday.
The two-year-old twins, who were born joined at the head, underwent marathon surgery on Saturday and Sunday to separate them and give them a chance at normal development.
Routine CAT scans of the boys' heads earlier on Monday showed no haemorrhage and only minimal swelling, according to hospital officials. A spinal fluid drain was placed in Muhammad's body in the morning. A similar one was placed in Ahmad's, right after the operation.
"The neurosurgical team is pleased so far," Thomas said. "But this is really an hour-to-hour, almost moment-to-moment thing right now."
Both Ahmad and Muhammad were listed in critical but stable condition as of 21:00 GMT on Monday.
They were resting in adjacent rooms in medically induced comas, in order to minimise the potential for brain swelling and were breathing with ventilators, the officials said.
To minimise the risk of infection and to keep their blood pressures even, the boys were receiving three antibiotics and other medication.
Doctors said that in two to three days, they would begin decreasing the dose of the barbiturates that keep each twin in a coma, and see how each responds.
"This is really an hour-to-hour, almost moment-to-moment thing right now"
head, critical care services, Children's Medical Centre
"When we can begin to withdraw the coma, that will end the medical paralysis that each boy is in and we'll be able to back off the ventilators," Thomas said. "At that point they will begin to resume their normal physical functions."
At the time of surgical closure on Sunday, Ahmad's wounds were completely covered by his own tissue. Muhammad had small areas at each temple that were not covered by tissue and eventually will require grafts, the officials said.
Ahmad and Muhammad were born in June 2001 and were immediately moved from their small town 800 km south of the Egyptian capital to the University of Cairo hospital.
The World Craniofacial Foundation of Dallas brought them to Texas in June 2002 and the surgical team studied their case for more than a year before operating.
In Cairo, the government magazine Al-Mussawar urged Egyptians on Monday to pray for the twins.
"Pray so that they return to Egypt safe and sound and they get well," the weekly said. "The hearts of millions of Egyptians are with them."