The man was apparently preparing to jump to his death when Erdogan's motorcade was passing over the bridge linking Europe with Asia after Friday prayers.
News footage showed Erdogan's bodyguards bringing the sobbing man, who appeared to be in his early 30s, to talk to him through the window of his car. After a few moments, the man can be seen kissing Erdogan's hand.
The man was then escorted to safety, the Dogan news agency reported.
It said police had been trying for almost two hours to talk the man out of committing suicide after he abandoned his car on the bridge and climbed over the side railing.
He has long been suffering from depression due to family problems, Dogan said.
The iconic bridge spanning the Bosphorus at a height of 64 metres (211 feet) is a frequent suicide spot.
