Mr Zitouni, 48, has been described as "nothing short of heroic" for his actions on the service from Doncaster to London King's Cross on Saturday evening.
British Transport Police said Mr Zitouni was "seriously ill" in hospital but his condition was stable.
Anthony Williams, 32, of no fixed address, has been charged with 10 counts of attempted murder in connection with the train stabbings and one count of attempted murder in connection with an attack in London on Saturday.
Mr Zitouni has worked for LNER for more than 20 years.
LNER Managing Director David Horne said: "In a moment of crisis, Sam didn't hesitate to step forward to protect those around him.
"His actions were incredibly brave, and we are immensely proud of him and all our colleagues who acted so courageously that evening.
"Our thoughts are with Sam and his family. We will continue to support them and wish him a speedy recovery."
Mr Zitouni is believed to have "intervened" to stop the attacker from stabbing a girl, who sustained injuries to her head and neck.
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In a statement, his family said they were "immensely proud of Sam and his bravery."
"The police called him a hero on Saturday evening, but for us, he has always been a hero." "We are so grateful for the love and kindness shown towards Sam and the well wishes for his recovery.
"The care provided by the hospital and the support from his colleagues at LNER has been fantastic."
On Monday morning, Transport Secretary Heidi Alexander said the bravery shown by Sam was "absolutely incredible" as he "put himself in harm's way."
"There are people alive today who might not be... if Sam hadn't done what he did."
Ten people on board the LNER train, which stopped in Huntingdon, Cambridgeshire, were taken to Addenbrooke's Hospital.
An eleventh person later went to the hospital.
Six of them have been discharged, and four remain in a stable condition.
The attack happened on the 18:25 GMT LNER service from Doncaster in South Yorkshire to London King's Cross station.
Passengers reported that after passing Peterborough, a man on the train pulled out a knife and began attacking people.
Cambridgeshire Police are investigating whether the man suspected of carrying out the attack is linked to an incident involving a 14-year-old boy in Peterborough and two reports of a man with a knife at a barber's shop in the city.
The teenager was stabbed on Friday, and a man was reported to have entered the shop with a knife. The shop made a second report the following day.