"Any manipulation of the results is shocking and goes against our fundamental values in sports... On behalf of the SUL, I present my sincerest apologies to those who have suffered injustices and to their families," SUL chairman Vesa Harmaakorpi said in a statement published late Wednesday.
A photo reprinted in the Finnish press recently showed Abraham Tokazier of Finland crossing the finish line first in a competition held to inaugurate Helsinki's Olympic Stadium.
But another Finn, Aare Savolainen, was named the winner of the race, and will go down in history books as such. Tokazier, initially declared the winner, was relegated to fourth position by the judges with no explanation.
Makkabi, the main Jewish sporting club in Finland, has long requested that the federation publicly admit wrongdoing.
"Overall, we're pleased with the admission that the official results were wrong, but apparently they will not be rectified," Makkabi chairman Ari Bensky told Finnish daily Helsingin Sanomat.
SUL said that according to the rules in force at the time, the finish line was judged by the naked eye and "the photos from the finish line were not available directly after the competition."
According to the association, the standings cannot be changed after the fact.
Although anti-Semitism was not a very widespread political ideology in Finland in the 1930s, there were "anti-Semitic sentiments like in most European countries," historian Oula Silvennoinen said.
He said SUL's apologies come after "repeated pressure" put on the association,
and noted that Finns "were long reluctant to examine or acknowledge events that took place in Finland during the German national-socialism era."
During the conflict between Finland and the Soviet Union in 1941 to 1944, Helsinki allied with Nazi Germany.
According to a comprehensive Finnish study carried out between 2004 and 2008, Finland handed over at least 59 Jews to the Nazis, most of whom died.