Jesus, the man, did not speak Greek. He spoke Aramaic and Hebrew. When he uttered the words "I am", he was speaking in Aramaic or Hebrew.
The Jews saw his claim as blasphemy. It happened again in John 10 when he said "I and the Father are one." The Jews again wanted to stone him -- "We are not stoning you for any of these," replied the Jews, "but for blasphemy, because you, a mere man, claim to be God."