Muamba's father and fiancee released a statement on Friday in which they thanked fans, football figures and medical staff for their support since Saturday, when Muamba collapsed just before halftime of Bolton's FA Cup quarterfinal at Tottenham.
The former England under-21 international is still at London Chest Hospital, where he was taken from Spurs' White Hart Lane stadium.
"Even though Fabrice has made great progress over the last couple of days, he is still in intensive care and still has a long period of recovery ahead," Marcel Muamba and Shauna Magunda said. "He has asked that you please keep him in your prayers."
Players across Europe have worn T-shirts expressing their support for Muamba.
European champion Barcelona is among the clubs to have made the gesture, while FIFA President Sepp Blatter has spoken with Bolton's chairman and asked to be kept informed of Muamba's progress.
"We have been overwhelmed by all the kind messages we have received," the statement said. "The support we have had from the fans — not just from Bolton but football supporters around the world — has given us so much strength.
"We have been particularly touched by the support from the football community globally."
Muamba has spoken to visitors at his bed side but it is too early to say if he will ever play professionally again.
Medics tried to revive Muamba for 48 minutes before he arrived at the east London hospital. Bolton team doctor Jonathan Tobin said it then took another 30 minutes, after 15 shocks from a defibrillator, before the player's heart started beating again.
The cause of the cardiac arrest has not been discovered. Doctors said that Muamba had undergone a routine screening for heart defects in August. He was checked again Sunday, with the test producing a normal result.Suggest a correction