He then told officers that he had shot dead another man at a location close to the Old City, police said.
In the first incident the man shot dead the Arab man after he "disturbed his meditation", a police spokesman was quoted as saying by the AFP news agency.
A short while later, he opened fire at two men wearing kippas, the Jewish religious skullcaps, after they asked him for cigarettes.
Rosen said that the man appeared to be mentally unbalanced.
"It seems to be that he has a psychological background," Rosenfeld said.
Shmuel Ben-Ruby, another police spokesman, said the wounded man had been hospitalised.