Steinmeier and other world leaders are in Poland to commemorate the outbreak of the conflict, the BBC reported.
Earlier on Sunday, a ceremony was held in the Polish city of Wielun, where the first German bombs fell.
At dawn on September 1, 1939, the German Luftwaffe (air force) bombarded Wielun, a town with no military significance. Thousands of people are estimated to have died in the bombings, designed to sow terror among the civilian population.
Steinmeier condemned the "desire to annihilate" that led to the attack.
"I bow my head before the Polish victims of Germany's tyranny. And I ask forgiveness," Steinmeier said, speaking in German and Polish.
Steinmeier spoke alongside his Polish counterpart, Andrzej Duda, who denounced Nazi Germany's attack on Poland as "an act of barbarity".
At the ceremony, which began shortly after 4 a.m., a minute's silence was observed in memory of the victims.
"Wielun was to show what kind of war it would be, that it would be a total war, a war without rules, a destructive war,"Duda said.
Later on Sunday, other world leaders, including German Chancellor Angela Merkel and US Vice-President Mike Pence, will gather for a ceremony in the Polish capital, Warsaw.
Steinmeier, Duda and Pence will deliver speeches at the ceremony in Warsaw's Pilsudski Square, the site of the Tomb of the Unknown Soldier.
Poland suffered some of the worst losses of World War Two: about six million of its citizens were killed, the BBC reported.
Eighty years on, Poland is still demanding compensation from Germany for the death and destruction inflicted.
( With inputs from IANS )