The Bolton midfielder began breathing independently again and speaking on Monday, two days after collapsing during an FA Cup quarterfinal at Tottenham, and medics said on Tuesday he had a "comfortable night" in intensive care.
"It's still very early in the process," Bolton manager Owen Coyle said after speaking to Muamba in hospital. "There is still a long way to go but there are encouraging signs ... and we pray he continues to improve."
Premier League chief executive Richard Scudamore said earlier Tuesday that "everyone comes out of this with huge credit," particularly the medics at Tottenham who immediately raced onto the pitch to try to resuscitate the 23-year-old Muamba.
But there will be a full review of the treatment available at White Hart Lane for the former England Under-21 international and the medical checks that footballers receive.
"Incidents and events shape policy, shape developments, shape progress," Scudamore said. "We will look at every aspect of what happened and ... if there are ways and means of making it better in the future. We will do everything we can to reduce to the point of elimination, if we possible can, things like that."
An ambulance was on hand on Saturday at White Hart Lane following criticism from then-Chelsea manager Jose Mourinho in 2006 about the time it took for goalkeeper Peter Cech to be transported to hospital after fracturing his skull during a game at Reading. An ambulance must be in place at stadiums for the exclusive use of players and club doctors.
"Jose Mourinho has made some strident comments about the X minutes it took for the ambulance to come," Scudamore told a Sport Industry breakfast in London. "It was a wake-up call, just things like having a dedicated ambulance for players and match officials ... in some ways, his life, if it is saved — and let's hope it has been saved — is as a result of the things a lot of us put in place after what happened with Petr Cech."
Medics are yet to reveal the cause of Muamba's cardiac arrest, but Manchester City manager Roberto Mancini on Tuesday said twice yearly medical screenings should be considered for Premier League players.
"We need to improve the medical side for the players," Mancini said. "We need to screen the players often, maybe two times a year and they have to be more accurate because they don't do this. When I saw our medical two years ago, I was really worried. I said we need to do them better ... what happened to Muamba and other players in the past can't happen again."
For two days, amid an outpouring of global support, Muamba remained in critical condition in intensive care in a heart attack unit in London, and his long-term prognosis was uncertain.
But the Congo-born player made progress throughout Monday, with medics no longer describing his condition as "critical" by the evening.
"He is continuing to show signs of improvement this evening," Bolton and the London Chest Hospital said Monday in a joint statement. "He is now able to breathe independently without the aid of a ventilator. He has also been able to recognize family members and respond to questions appropriately.
"These are all positive signs of progress. However, his condition remains serious and the medical staff in intensive care will continue to monitor and treat him."
Rob Harris can be reached at www.twitter.com/RobHarrisUK