Spain midfielder Andres Iniesta stepped up his recovery from a minor thigh muscle strain on Saturday but remains a doubt for the European champions' opening Group H match on June 16.
Iniesta is a key component of Vicente del Bosque's squad and produced a sparklingly creative performance in Tuesday's 6-0 thumping of Poland in a friendly international before being forced off.
A scan the following day showed there was only slight swelling and no tear.
"Andres is progressing very well with the minor muscular problem he sustained," chief doctor Oscar Luis Celada told television station Telecinco after Saturday's training session at Spain's training base in Potchefstroom.
"We still don't know if he'll be fit for the Switzerland match (on Wednesday) but the feelings are positive," he added.
"There are still a few days before the World Cup starts for us and there is time to decide."
Iniesta trained apart from the rest of the 23-man squad for a second day at a sun-kissed North West University on Saturday and was able to complete some more intensive ball work after light jogging around the specially-laid pitch.
If he is not ready for Spain's opening match against the Swiss, Del Bosque has a wealth of talent to replace him in the starting lineup, including David Silva, Pedro and Juan Mata.
"Andres is extremely important for us," Silva said at a news conference after Saturday's session.
"Thank goodness he is recovering and the sooner he is back the better. He is a great player and he gives us a lot of joy."
A string of top players have been forced out of the World Cup with injury and Spain defender Alvaro Arbeloa said the squad were crossing their fingers they would be spared.
"Injuries are part of the world of soccer and all sports and sometimes you can't do anything about them," he said at the same news conference.
"But we are 23 players and if someone gets injured we definitely have good alternatives to replace them," he added.