Miles Hurley, 21, was rushed to hospital after being stabbed "several times" in Nine Elms, south west London.
London Ambulance Service took the two men to a south London hospital, where they were treated for stab wounds.
Elizabeth spoke out on Twitter on Saturday morning to thank fans for their messages during this hard time.
The 52-year-old star flew from the U.S. as model Miles Hurley, 21, was fighting for life following the attack in a London street.
"He was repeatedly stabbed and lost more than four pints of blood", she wrote.
Police have reassured family members and the public that their conditions are "not life-threatening or life-changing". The police & hospital are being fantastic. Our hearts are with Elizabeth and her family during this time. The police will be appealing for witnesses'.
"His family feared the worse", said a source close to the situation. "Fortunately.it seems the knife missed his vital organs".
It is believed the men were attacked by a group of men who jumped from a vehicle, assaulted them, and took off.
The 52-year-old star of The Royals was pictured landing at Heathrow Airport on Friday and is said to have flown back from the U.S. where she was promoting the show to be with him.
Miles' mum is Liz's older sister Kate Curran, and the model is very close to his aunt Liz.
On the day of the attack, Miles had paid tribute to his aunt in a post celebrating International Women's Day. It is the sole responsibility of each user to ensure they are completely happy to interact and trade with each on-line fashion vendor.
Miles started his modelling journey at the age of 13, and landed modelling work with Dolce & Gabbana and Roberto Cavalli.
Miles has spoken publicly before about his close relationship with Liz, saying "I'm really close to my aunt and she's very supportive of everything I do".