Michael and Nan MacIntyre said their daughter “is amazing us every day with her strength and determination” as she is treated in hospital.
The couple said the 15-year-old had “sustained horrendous injuries”, but has now been taken off a ventilator and is able to talk to them.
Laura, from Barra, in the Outer Hebrides, was at the Ariana Grande concert with friend Eilidh MacLeod.
The Castlebay Community School pupils were reported missing after they failed to get in touch with family following the explosion.
It was later confirmed that Eilidh was among the dead, while Laura was found in hospital.
In a statement, Laura’s parents said: “We have been overwhelmed by the love, help and support from everyone. It means so much to us.
“Laura sustained horrendous injuries. The main worries being head and leg injury.
“She is making remarkable progress. Today she came off the ventilator and is talking and recognising us. She is amazing us every day with her strength and determination.
“We have a long way to go but we are going in the right direction. We are so lucky to have her. The hospital and the staff are amazing.”
The couple added: “We only wish that Eilidh was here too, our hearts and thought are with Eilidh’s family.”
In a statement released at the weekend, Roddy and Marion MacLeod said: ‘’We continue to have Laura and her family in our thoughts and pray that she makes a full recovery.”