The 23-year-old paramedical student was flown into Singapore from New Delhi, where the attack occurred last week, to seek further medical treatment here.
She had already undergone three abdominal operations and suffered a cardiac arrest in India.
Mount Elizabeth Hospital chief executive Kelvin Loh said in a statement yesterday that a multi-disciplinary team of specialists was "doing everything possible to stabilise her condition". As at 7pm, she remained in an extremely critical condition, he said.
The victim, who has not been named, was put on a Singapore-bound air ambulance at about 2am yesterday. She was accompanied by her parents, two brothers and a team of Indian doctors led by Dr Yatin Gupta, head of the critical care unit at New Delhi's Safdarjung Hospital, where she was treated earlier.
The Indian Cabinet made the decision to fly her and her family at government cost to Singapore based on the advice of a team of government and private doctors.
The group arrived at Changi Airport shortly after sunrise yesterday and were whisked off to Mount Elizabeth Hospital, off Orchard Road, within minutes.
The victim arrived at the hospital's intensive care unit (ICU) by 9.05am and was quickly attended to by medical specialists. Security was tight at the hospital, favoured by well-heeled patients, with each visitor screened before being allowed into the ICU.
Police officers were also seen at the ward later in the afternoon.
A source who met the victim's father and two brothers yesterday told The Straits Times the family is shell-shocked, but thankful. "Aside from the trauma of the rape, they also have to get used to the idea that they are now in a foreign land," said the source, who asked not to be named.
"These are simple, rustic people who have never dreamt of boarding an aircraft, much less travel to a foreign country in an air ambulance."
He added that the father, who is in his late 40s, repeatedly expressed his gratitude to the Indian government and Singapore for facilitating the travel and treatment. "The father said he is reassured that the best is being done for his daughter, and the rest lies in the hands of God," he said.
The Straits Times understands that the family members do not speak English and rely on interpreters to communicate with hospital staff.
The Indian High Commission here has provided them with chaperones, mainly to help them travel from the hotel to the hospital.
Several Indian officials, including Indian High Commissioner to Singapore T.C.A. Raghavan, visited the victim and her family at the ward throughout the day.
The victim was raped on Dec 16 by six men on a bus, after she and a male companion boarded it to go home after a movie.
The suspects, who have been arrested, allegedly raped her, then stripped her before throwing her and her male companion, who was also beaten, out of the bus.
It sparked days of protests, including violent clashes, with protesters demanding justice for the victim. The situation ebbed only after 47-year-old police constable Subhash Chand Tomar died on Tuesday morning from injuries sustained during the protests.