The Bolton midfielder began breathing independently again and speaking two days after collapsing during Saturday's 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."
Coyle hopes the 23-year-old Muamba, who fled to England from Congo's civil war in 1999, will one day return to action.
"It is something which has happened before," Coyle said. "There are two things which might help — he is such a fit young man and in the life that he has had he has needed to fight every step of the way."
Premier League chief executive Richard Scudamore said 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 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.
"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."
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."
But the Professional Footballers' Association disclosed that it has spent around $10 million over the last 20 years on screening professional footballers for heart defects.
"In the immediate aftermath of Saturday night, we checked Fabrice's records and he had been screened four times," PFA chief executive Gordon Taylor said. "What they have in Italy is government-funded. In England the PFA does it. The truth is even if you screened someone every three months, there may be some things that wouldn't get picked up."
For two days, amid an outpouring of global support, Muamba remained in a critical condition in intensive care in a heart attack unit in London, and his long-term prognosis was uncertain.
But the Congo-born player has continued to make progress, with medics describing his condition as "serious" instead of "critical" and being able to communicate with bedside visitors.
Bolton's Premier League match at Aston Villa scheduled for Tuesday was called off the day after Muamba collapsed and the club plans to decide on Wednesday whether to go ahead with Saturday's fixture against Blackburn.
Rob Harris can be reached at www.twitter.com/RobHarrisUK