The left-wing official called for Europeans to remain united in the face of right-wing nationalism.
He made the comments shortly before Frank-Walter Steinmeier, his successor, was elected as the country’s new president.
Mr Gauck said: “The European Union is not ‘existentially threatened,’ as some might say.
Former German president, Joachim Gauck, argued the European Union is not about to collapse
“Anti-EU campaigners – a tiny minority – want it to be, of course they do. They claim that the EU is ‘a sham,’ but they’re wrong.
Mr Gauck, a former Protestant pastor, added that Germany’s devotion to the Brussels bloc did not stop officials and citizens from “questioning” the value and future of the EU.
Mr Gauck does not believe Brexit will bring down other nations with it
He said: “People fear that immigration and globalisation will distort their culture and identity. We need to ask them what they are afraid of exactly and do everything in our power to allay their fears.”
The outgoing president, however, said that he did not believe that "Hitler-like" populist leaders would “take over” Europe.
He said: “Pope Francis warned the world against the rise of populist leaders like Adolf Hitler; but I disagree with his comments and with his assessment of the current political situation. Things were very different back then.
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“More and more people are speaking out in defence of democracy. Demagogic nationalists spread fear and prejudice; but in the end, democracy will trump populism.”
Anti-EU campaigners – a tiny minority – claim that the EU is ‘a sham,’ but they’re wrong
When asked to comment on Britain’s startling decision to leave the 28-member bloc, Mr Gauck said that Brexit would “not” trigger a ‘domino’ effect in Europe.
“I very much doubt that the Brexit vote will trigger a ‘knock-on’ effect and prompt other member states to renegotiate their relationship with Brussels. There’s too much at stake; remaining member states have too much to lose.”
Mr Gauck, a former human rights activist, also commented on the ongoing migrant crisis, and voiced hope that the EU would come up with a “common” immigrant policy.
The politician hopes the EU can work out better controls on immigration
He said: “We must do more to secure EU’s external borders. I’m not saying that we should stop refugees from entering the EU. But we do need greater control over immigration.”
Mr Gauck also said that German Chancellor Angela Merkel could not be blamed for the 2015 refugee crisis.
He said: “Mrs Merkel’s open-door immigrant policy is not to blame. Refugees would have poured into the EU regardless of her policies. We, as European citizens, must now help refugees integrate into European society.”
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