Steinmeier and his host also called for a “new chapter” in bilateral relations, to leave behind tensions caused by tough German demands for Greek austerity to accompany EU bailouts for Athens.
Noting Greece is on the front line of migration flows to Europe, Steinmeier said any “consensus” on migration policy “is not possible without solidarity”.
He said he shared Tsipras' fears over the dangers that nationalism could pose to the future of the bloc.
“We must take steps to convince European citizens that is it possible to emerge, together, from crises – we must keep extreme and populist voices at bay,” he said.
Tsipras said Greece wanted to move on from the “difficult moments between our two countries during the (financial) crisis… and the stereotypes which poison our relations”.
German insistence on financial rigour and eight years of austerity measures to accompany three EU multibillion rescues of the Greek economy soured relations in a country which has not forgotten the Nazi-era occupation during World War II.
“We are at a moment where we can open a new page in our relations,” Steinmeier said.
Relations have improved over the last three years after Tsipras' government endorsed conditions linked to satisfying its creditors and Tsipras and German Chancellor Angela Merkel also worked closely on finding common ground on migration.
Tsipras did not mention the thorny issue of war reparations, which Greece has been seeking since the 1990s, despite the impending publication of a report by his leftist Syriza party understood to want around 270 million euros ($312 million) from Berlin.
However, Steinmeier, who arrived on the eve of the 1944 anniversary of the liberation of Athens, commented that “we ask forgiveness for atrocities” committed and “we do not want to forget the past”.
Berlin's official position is that the issue was definitively resolved in a previous, wider post-war agreement with a number of countries, including Greece.