A request calling for Ms Albayrak to be gave the state order for merit afterwards has grouped over 100,000 signatures.
Authorizing he would ponder the award, President Mr Gauck wrote to her family to say: "Like uncountable inhabitants, I am surprised and shocked by this dreadful act. Tugce has made appreciation and admiration from us all.
"She will permanently remain a role model to us; our entire country sorrows with you.
"Where other people observed the other way, Tugce showed model bravery and ethical determination."
Before Sunday's "civil courage" wake on Oranienplatz in Berlin, honors were rewarded in Offenbach, with people stock symbols which speak "Thank you, Tugce".
Oranienplatz is in the core of Berlin's Kreuzberg district, which has a large Turkish community. Ms Albayrak, who was from the town of Gelnhausen, also near Frankfurt, was Turkish by basis.
Her aggressor, termed only as Senal M from the Sandzak area of Serbia, has confessed to salient Ms Albayrak, German public radio staion Deutsche Welle confirmed.
Germans honour slain 'role model' Tugce Albayrak
Germans honour slain 'role model' Tugce Albayrak
Germans honour slain 'role model' Tugce Albayrak
Image : Source