The closest the planes came to each other was 300 feet vertically and 1,500 feet horizontally, Gregor said. The United flight continued to Beijing with no further incident.
According to Gregor, air traffic controllers cleared the United flight, a Boeing 777 carrying 251 passengers, for takeoff at 11:15 a.m. and quickly spotted the Cessna 182 flying south.
The controller radioed both planes' pilots, Gregor said, and the jet's automatic traffic collision avoidance system alerted its pilots of the small aircraft approaching, causing them to level the jet's climb.
"The Cessna pilot reported that he had the 777 in sight, and adjusted his path to maneuver above and behind the 777," Gregor told The Associated Press in an e-mail.
United spokeswoman Robin Urbanski said the airline is fully cooperating with the investigation and that it reported the incident to NTSB. She said this kind of near, mid-air collision is "unusual" for United.
Gregor said the controller should have noticed the Cessna earlier, but noted that the pilots were quickly contacted once the situation was recognized.
David Caldwell, union representative for the National Air Traffic Controllers Association at the SFO tower, had no immediate comment on the investigation.
"We have to go through a process to make a fair evaluation of what happened, and if we need to fix something, we fix something," Caldwell said.
Gregor said the FAA does not keep statistics on near misses, and that they are reported by pilots. However, he said misses this close are rare and need to be properly scrutinized.
NTSB spokesman Peter Knudson said its investigation could take three to 12 months.
"If we determine at any point in the investigation that there was a serious safety issue ... we can issue safety recommendations," Knudson said.