"Michael Ballack has earned an honorable farewell, despite what has happened (in the past days). What Low offered him was an honest offer," DFB president Zwanziger said.
Ballack was furious to learn on Thursday that his international career was ending when Loew said he was not counting on the 34-year-old Bayer Leverkusen midfielder any more.
Low, who said a string of younger players were now the backbone of his team, said Ballack had understood his point of view in their one-on-one talks.
The following day, Ballack accused the coach of telling "things that are distant from the truth" and said he had been assured by Low that when he was fit after an injury that ruled him out of last year's World Cup, he would be recalled.
Ballack called the proposed farewell match against Brazil on August 10 a 'farce', saying the game had been scheduled by the federation long before he was informed of Low's real intentions.
After further angry exchanges over the weekend, Zwanziger said Ballack's choice of words had been too strong.
"But we do not bear grudges. The DFB door remains open for him. I think it is a great gesture for the long-time Germany captain to say goodbye to the team and fans in a classic match against Brazil," he wrote in a column to be published on Wednesday in Sport Bild magazine.
"Michael Ballack obviously thought he still had a shot at playing in next year's Euro (in Poland and Ukraine) - possibly even as team captain. It is only logical that the decision of the coach is painful."
Ballack, who has scored 42 goals in 98 internationals since making his debut in 1999, has not played for Germany since March last year after sustaining an ankle injury that forced him to miss the 2010 World Cup.
Germany finished third in that tournament in South Africa after fielding their youngest World Cup team in 76 years.
