"We've had a very, long, intense conversation and we want to get this misunderstanding out of the way," Low told a news conference today alongside DFB president Theo Zwanziger and national team manager Oliver Bierhoff.
"We are united in that our common interest in the next few weeks is the World Cup, where we have an unbelievably big responsibility."
Zwanziger said in December that Low had verbally agreed terms to extend his contract for two years after the World Cup in South Africa in June. Low denied last week there had been any such agreement.
Last Thursday, Zwanziger said the two sides had been unable to agree on some aspects of the contract and negotiations had been set aside while the team prepared for the World Cup.
His comments led the media to speculate on a power struggle within the DFB and the issue has filled the sports pages of Germany newspapers since last Thursday, although there was never any suggestion of Low quitting his post.
On Tuesday, both sides said they had agreed only to discuss a contract extension after South Africa, where Germany, one of the favourites, face Ghana, Australia and Serbia in Group D.
"We have to remember that we are representing not only the DFB but also Germany and millions of fans," said Low.
"I can assure you that we will do everything that so that Germany does well at the tournament."
Zwanziger added: "We want success and I think that success is only possible with this coach."
Low took over from Jurgen Klinsmann following the 2006 World Cup and led Germany to the final of the European championship in Austria and Switzerland two years ago.
On Friday, he said he and Bierhoff had been handed a non-negotiable offer by the DFB and have been given only 48 hours to make a decision. He denied that the two sides had shaken hands on a new contract the previous December.
On Sunday, he said he was "very angry" that details had come out into the open.
Unbeaten in their last 10 outings, Germany have played 45 games under Low with 31 wins, eight draws and six defeats.
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