Steinmeier stuck to his guns on Friday, arguing in an interview with Spiegel that "We in Germany need to be careful not to give justification to those who follow their own political agenda and say the Holocaust started before 1933.'"
"I'm tired of debates in which I'm expected to jump over a stick which is being held out for me, although everyone knows that complex memories can rarely be brought together under one word," the foreign minister said.
"The simple reduction of this debate to the question of whether we describe it as genocide or not" doesn't help "end the silence that persists between Turks and Armenians."
Steinmeier has come in for fierce criticism this week, with one high profile politician comparing him to Germany's First World War leadership.
Both Gauck and Bundestag (German parliament) president Norbert Lammert condemned the massacre of 1.5 million Armenians by Ottoman forces a century ago as a "genocide", the first time Germany has officially used the term.
Gauck's speech at an event commemorating the centenary marked the first time that Berlin has officially used the word "genocide" to describe the killings in Armenia, and an unusually strong acknowledgement of the then German Empire's role.
"In this case we Germans must come to terms with the past regarding our shared responsibility, possibly shared guilt, for the genocide against the Armenians," he said at the ecumenical service in Berlin.
He was joined in using the word genocide by Bundestag (German parliament) president Norbert Lammert.
Lammert opened a debate on Armenia in the chamber by saying that "what happened in the Ottoman Empire before the eyes of the world was a genocide. It did not remain the last one of the 20th Century.
"That makes our obligation not to repress or gloss over the crimes committed then that much bigger, out of respect for the victims and with responsibility for cause and effect."
Armenians say up to 1.5 million of their kin were killed between 1915 and 1917 as the Ottoman Empire was falling apart and have long sought to win international recognition of the massacres as genocide.
Modern Turkey, the successor state to the Ottoman Empire, rejects the claim, arguing that 300,000 to 500,000 Armenians and as many Turks died in civil strife when Armenians rose up against their Ottoman rulers and sided with invading Russian troops.
Gauck's statement was expected to draw an angry reaction from Ankara, which has close defence and trade ties with Berlin.
Germany also has a three-million-strong ethnic Turkish population deriving from a massive "guest worker" programme in the 1960s and 1970s.
Turkish Foreign Minister Mevlut Cavusoglu said earlier Thursday that a decision by Austrian lawmakers this week to condemn the massacre as "genocide" would have "unfavourable repercussions" for bilateral ties.
Gauck, a Protestant pastor and former East German dissident, is the head of state and serves as a kind of moral arbiter for the nation.
Nazis banned book
In his speech at the Berlin Cathedral, Gauck said that particularly given Nazi Germany's slaughter of six million Jews during World War II, for which Berlin has publicly atoned for decades, it must also own up to its historical guilt in the Armenian mass murders.
"Woman and men, children and the elderly were indiscriminately sent on death marches, banished without any protection or food to the steppe and the desert, burned alive, chased, beaten and shot to death," he said.
"This planned and calculated criminal act targeted the Armenians for a sole reason: because they were Armenians."
Gauck said that the German empire, then allied with the Ottomans, deployed soldiers who took part in "planning and, in part, carrying out the deportations".
German diplomats and observers who reported back to Berlin the atrocities they witnessed were "ignored" for fear of jeopardising relations with the Ottomans, he said.
Gauck said that the Nazis even banned an Austrian novel about the mass murders but that the book was read in Jewish ghettos in the 1930s "as a harbinger of what was to come for the Jews".
He said it was impossible to walk away from guilt through "denial, repression or trivialisation" of history.
"We in Germany learned the hard way, in part by shameful procrastination, to remember the crimes of the Nazi era, above all the persecution and extermination of European Jews," he said.
The presidents of Russia and France - two of nearly two dozen countries to formally recognise the genocide - are to join a handful of world leaders attending a commemoration of the massacre in the Armenian capital Yerevan on Friday.
Germany plans to send a junior foreign minister to the event.
While Gauck clearly labelled the mass murders a genocide, the German government has backed a compromise resolution to be debated on Friday in parliament.
"Their fate exemplifies the history of the mass murders, ethnic cleansing campaigns, expulsions, indeed the genocides that marked the 20th century in such a horrible way," reads the draft text obtained by AFP on Monday.