Medical staff took two hours to get Muamba breathing again and he is now being closely monitored in the Heart Attack Centre at The London Chest Hospital.
A joint statement from Bolton, Barts and The NHS Trust read: "Fabrice Muamba's heart condition is stable, but he remains critically ill in intensive care at The London Chest Hospital. The family is grateful to the media for continuing to respect their privacy at this time."
Bolton manager Owen Coyle and chairman Phil Gartside visited the hospital on Monday morning.
Coyle, who accompanied Muamba to hospital, offered his personal thanks for the messages of support that continue to be received, both at the hospital and the Reebok Stadium.
"From our end, and on behalf of the family, we want to say a big thanks to everyone," said Coyle.
"We have been inundated by good messages, everyone praying for Fabrice which is very important. It has been a real source of strength for the family. We know how difficult a time it is for everyone.
"I can't really quantify it (the support). It has been incredible, not just from the football world, from everyone.
"It is great to be talented at football but it's more important to be a genuinely nice man and everyone recognises Fabrice is that.
"That has pulled everyone together. We certainly hope he comes through this. If he pulls through it would be marvellous, it really would."
Source: PA
Source: PA