The country's leading role in setting conditions for bailing out profligate eurozone states has sparked anti-German sentiment across southern Europe, with some drawing parallels to the Nazi era when Germany invaded much of the continent.
In a keynote speech setting out his vision for the continent, Mr Gauck, 73, a former Lutheran pastor and human rights activist in Communist East Germany, urged people to look beyond the eurozone crisis and political upheavals, and to see Europe as a community of shared values.
He said: "It worries me when the role of Germany in Europe apparently causes scepticism and suspicion in some countries."
The President claimed it shocked him how quickly the nation could be viewed "in a long tradition of German power politics, even German crime".
In countries such as Greece and Spain, protesters have blamed German Chancellor Angela Merkel for saddling them with punishing austerity policies and plunging them deeper into recession.
The sight of Nazi flags being burned or pictures of Ms Merkel festooned with swastikas is commonplace. Thousands of Greeks protested during her visit there last year and a German diplomat was pelted with water bottles in the northern city of Thessaloniki.
Comments in 2011 by Volker Kauder, parliamentary leader of Ms Merkel's Christian Democrats, that "Europe is speaking German" caused unease about how Berlin would wield its economic might.
But Mr Gauck said: "I assure all citizens in neighbouring countries, I see nobody within the German political class who wants to push a German diktat.
"From my own deep conviction I can say: more Europe does not mean in Germany a German Europe. Rather it means for us a European Germany."
The President wields little political power but has moral influence. Speeches by predecessors such as Roman Herzog and Richard von Weizsaecker proved influential in shaping German consciousness and identity.
"We don't want to intimidate others, nor force our ideas upon them. But we do stand by our experiences and want to share them. Less than a decade ago Germany itself was the 'sick man of Europe'," said Mr Gauck.
A prominent player in the peaceful protests that led to the fall of the Berlin Wall in 1989, his election was met with hope that he could restore dignity to a post tarnished by financial scandals that toppled his predecessor Christian Wulff.
Ms Merkel only reluctantly endorsed his candidacy after her Free Democrat coalition allies joined opposition parties backing him. Mr Gauck poses no threat to her domination of German politics but his lack of party affiliation allows him to speak out freely.
He called for the concept of "more Europe" – something of a mantra for Ms Merkel – to be clearly defined so that citizens feel more engaged with a stronger common identity that would help the bloc stand on its own in an ever globalising world.
"Europe is too little prepared for this. We need further inner union. Without common financial and economic policies our common currency will only survive with difficulty. We also need further union in our foreign, security and defence policies."
Mr Gauck also appealed to the UK to stick with Europe.