An update posted on the hospital website at 10:30 on Saturday (03:30 GMT on Sunday) said the main phase of the operation, the neurosurgical phase, was continuing, and listed the boys' condition as stable.
The procedure began at the Children's Medical Centre in Dallas, Texas early on Saturday. Doctors are now predicting it could last into Monday.
Ahmad and Muhammad Ibrahim, born in a small town 800 kilometres south of Cairo, have lived in Dallas since June 2002, where doctors have been observing them for more than a year.
They say the boys' brains are almost completely separate, or only minimally joined. But they share a complex network of blood vessels which must be divided one by one.
"Our sense is we're probably dealing with 50 to 100 veins," Kenneth Shapiro, one of five paediatric neurosurgeons participating in the operation, explained earlier.
If after seven days "they're awake and moving arms and legs on both sides, I'm going to be real happy"
Attending physician Jim Thomas told a televised press briefing on Saturday that the neurosurgical portion of the operation had begun shortly before 15:00 (20:00 GMT), after lengthy preparation procedures.
"Everything is going fine and there have been no problems," he said. "And that's the information that I have from the operating room."
Benefits outweigh potential loss
The operation is extraordinarily risky, but after studying the twins at length, surgeons became convinced that the benefits of a successful separation outweighed the progressive loss of function the boys would face if they remained conjoined, Thomas said.
The operation will ultimately involve more than 40 doctors, nurses, and other hospital staff, working in shifts.
Dr Jim Thomas told reporters that
the operation is going well so far
The boys' parents are in seclusion and receiving hourly updates on the operation. They arrived in the US a week ago, after visa delays postponed the surgery.
Their mother had not seen them since they left Egypt more than a year ago, accompanied by two Egyptian nurses.
Their father was with them from October 2002 to June 2003, but had returned to Egypt to see his wife and two other children – a six-year-old son and a seven-year-old girl.
The boys' medical care has been funded by public donations. If they survive, they will still need months of therapy to help them recover and learn to function separately.
The boys were put under anaesthesia early on Saturday morning. If the operation is successful, doctors will keep them in a drug-induced coma for another week to reduce brain swelling.
If after seven days "they're awake and moving arms and legs on both sides, I'm going to be real happy," said participating neurosurgeon David Swift.