No one was injured.
The retired Anglican archbishop from South Africa had just left St. Mark's Episcopal Cathedral after a Thursday night service when the man approached him, Officer Deanna Nollette said.
Tutu handed the .45 caliber bullets to another person and continued to his car. The other person turned and gave the rounds to a Seattle police officer on scene for crowd control, she said.
The "alarmed" officer approached the man who handed out the bullets, patted him down and found a .45 caliber handgun, a fixed blade knife and additional ammunition in the man's fanny pack, Nollette said.
Nollette said the 57-year-old Seattle man, who had no concealed weapon permit, was found to be a convicted felon and was arrested without incident for investigation of a weapons violation.
She said she had no specific information on his record.
Nollette said she did not know what the man said to Tutu, who had been in Seattle for a two-day visit.
"I think we are incredibly fortunate and blessed that the bishop and no one at the event was injured, because obviously the suspect had the opportunity and the firepower to do that if that was his intent," she said.
Tutu, a Nobel Peace Prize laureate, had been in town for the 75th anniversary of St. Mark's. He is a personal friend of the Very Rev. Robert Taylor, dean of the cathedral.
The Rev. Peter Strimer of St. Mark's said people in a crowd outside the cathedral had been talking to Tutu when the man approached, spoke to him and gave him the bullets.
Strimer said Tutu was not threatened and said the incident "in no way will every stop him from reaching out to the people."
Tutu fought against apartheid in his homeland.
The archbishop, who has left Seattle, was not immediately reachable for comment Friday night.