Lahm's comments in an interview with the newspaper Bild, were published on Tuesday and team manager Oliver Bierhoff had to answer a series of questions about the issue - and the departure of Ballack from the team camp.
Bierhoff denied that the controversy, which broke out just over an hour before the German team were due to fly to Durban for their Wednesday semi-final with Spain, had upset the team.
"There is no dissent whatsoever, not even a hint of conflict," he told a news conference at the team's hotel.
Lahm is officially the World Cup captain while Ballack, who recently moved from Chelsea to German club Bayer Leverkusen, remains the team captain.
Ballack, who has missed the tournament due to an ankle injury, flew out to be with the team ahead of the quarter-final with Argentina but returned to Europe on Monday prompting speculation he may have been upset with Lahm's comments.
"It's not the case, Ballack visited the team in Sicily before the tournament and it was always agreed that he would visit for the quarter-final.
"UNFORTUNATE COINCIDENCE"
"It is an unfortunate coincidence that Ballack's departure and Lahm's statement coincided," Bierhoff told a news conference, adding that the midfielder's return was because he needed to continue his treatment on his ankle.
"He felt good and had excellent physiotherapy, luckily his injury is healing surprisingly fast... he needs a lot of rehab now, he needs special facilities and a lot of time.
"It emerged that Michael didn't want to take out any resources from the team. He knew that if his rehab was to proceed he needed more time from staff... he decided that it was better to continue treatment in Luxembourg," said Bierhoff.
Former AC Milan and Germany striker Bierhoff said that Ballack may return to South Africa if Germany reach the final.
In the comments to Bild, Lahm said: "It's obvious that I'd like to keep the captain's armband. The job gives me a great deal of enjoyment. Why should I then give it up by choice?
"If you do the job out there on the pitch and you have it under control, as in my case, you want more. You want more responsibility. You want to take care of it all. That is the case with me," he added.
Bierhoff said: "We have freedom of speech in the team and need players willing to speak their mind. It is rather like when a player says he is disappointed to be left out -- are you supposed to be annoyed that he is disappointed?
"But in the end, it is the coach who makes the decision over who is captain."
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