The man had climbed over a railing on the Bosphorus bridge linking Europe with Asia and was threatening to kill himself.
Mr Erdogan's motorcade was crossing the bridge at the time.
Television pictures showed Mr Erdogan's staff asking the sobbing man to talk to the president. After a few moments, he was escorted to safety.
The man was suffering depression due to family problems, and police had been trying to prevent him from jumping for some two hours, the Dogan news agency reported.
Footage shows officials persuading him to go and talk to the president in his car.
Mr Erdogan does not leave his car, and he speaks to the man with his mobile phone pressed to his ear.
An official from the president's office told Associated Press news agency he had promised to help him.