The 23-year-old remains critically ill in intensive care at the London Chest Hospital but his heart is now beating without the help of medication and he is moving his arms and his legs.
The statement added that Muamba's long-term prognosis remained unclear and that he would continue to be closely monitored.
Muamba collapsed on the pitch where he was given CPR (cardiopulmonary resuscitation) before being taken to hospital.
FIFA President Sepp Blatter was among those to offer support for the England Under-21 international with a letter to Bolton chairman Phil Gartside.
"On behalf of the worldwide football family, I would like to express my shock and distress on hearing about the cardiac arrest suffered by Fabrice Muamba during Saturday's FA Cup tie and wish him strength as he continues to fight to recover from this critical condition," Blatter wrote.
"Moments like these show us what is truly important in life and also illustrate the great solidarity that exists between football fans in times of trouble."
Bolton captain Kevin Davies told the club website the players had been overwhelmed by the reaction following Muamba's collapse.
"We all owe a big thank you to everyone that was on the scene; the paramedics and medical staff from both our club and Tottenham Hotspur. I've been at the hospital with the chairman and the manager, and we're all thankful for the amazing help and support everyone has shown for Fabrice," Davies said.
"Fab is not only one of our colleagues and a workmate but he's a friend, father and son - he's one of life's good guys.
"I think I was in the same position as everyone else. We were following the play and suddenly someone said 'Fabrice has gone down'. Then it all unfolded from there really. It became very serious within a matter of seconds," added the Bolton striker.
"I think it was the first time in my 19 years as a professional that I've seen a football stadium unite. It was touching."
Supporters from both clubs sang Muamba's name at White Hart Lane when it became clear his condition was serious while players gathered round in shock.
The match was abandoned at 1-1 just before half-time and Bolton's game with Aston Villa on Tuesday has been postponed.
Tottenham players have been offered extra heart checks following the incident, Spurs manager Harry Redknapp said.
"We will be providing players with whatever support they need in order to help them move on from what has happened while obviously always keeping Fabrice at the forefront of our minds and willing him to make a recovery," he told the Tottenham website.
"We already had a cardiologist visiting the training ground today for routine screening so we are able to offer any player who wishes to be tested for the purpose of reassurance an additional opportunity to be screened."
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