"The time for dialogue has arrived", he declared, condemning the "violent and repressive response" the push for secession has received from the Spanish government.
Puigdemont can still be extradited on the less serious charge of misuse of funds to hold Catalonia's banned independence referendum a year ago.
The speaker of Catalonia's regional parliament has again put forward a jailed separatist activist to be elected as the northeast Spanish region's new leader. He could still be extradited to Spain on charges of misusing state funds.
Puigdemont, who was released on bail from a German prison Friday, says he hopes a German court's decision to not extradite him to Spain on charges of rebellion shows that "dialogue is needed" to defuse the political conflict in his home country.
A smiling Puigdemont emerged into the sunshine from the prison in Neumuenster, where he has been held for almost two weeks, thanking staff "for their professionality and for their respect" and the inmates for "their solidarity and help for me to adapt quickly to the situation".
"This opens a new opportunity of dialogue".
Puigdemont, who fled Spain five months ago for Belgium after his administration's declaration of independence from Spain led to Madrid taking direct control of the regional government, was arrested last month on a Spanish-issued warrant as he entered Germany.
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At a press conference, a German government spokeswoman reiterated Berlin's position that it will not interfere in the judicial process, saying: "The proceedings are in the judiciary's hands".
The Schleswig prosecutor's office said Puigdemont was given an address in Germany, where he will reside until judges decide on Spain's extradition request.
Katarina Barley told daily Sueddeutsche on Saturday the judges' decision was "absolutely right" and what she'd expected.
He says the Spanish government "met its obligations" by imposing direct rule on Catalonia after Puigdemont and other separatists organized the independence referendum a year ago.
Ms. Barley claimed that it was now up to Spain to prove that their additional prices against Mr. Puigdemont, which she said "won't even be more easy".
Barley said it was now up to Spain to prove their embezzlement charges against Puigdemont, which she said "won't be easy".
Puigdemont could still face extradition on the other charge of misuse of public funds.