Tension soared when one of the animals charged a man and tossed him on the ground with its horns for almost 30 seconds as fellow runners tried to pull it away by its tail. The man clung to one of the horns as screams of were heard all around.
Helpers eventually dragged the victim to safety by his feet. The local Diario de Navarra newspaper said the man was from Morella, Spain, but this could not be immediately confirmed.
The regional government of Navarra said one American and two Spaniards were gored in the run while another American and two Spaniards were also taken to city hospitals for other injuries suffered in falls and trampling during the frenzied event.
The government press office identified the American gored only by his initials P.E. and gave his age as 20. The local paper said he was injured in the abdomen.
None of the six taken to the hospital was said to be in serious condition.
Hospital authorities initially said four people were gored but the regional government revised that down to three.
The gorings were the first of this year's runs, during which thousands of thrill-seekers race daily with the bulls along a 930-yard (850-meter) route from a holding pen to the city bull ring.
Friday's event lasted just under five minutes, roughly double the normal length. Longer runs normally occur when some of the bulls get separated from the pack and become disoriented and more dangerous.
The black bull which caused most panic Friday made several more attempts to charge people before he was eventually guided along the narrow streets to join the rest for the pack in the pen of the packed bull ring.
The nationally televised 8 a.m. runs are the highlight of the nine-day street partying festival made world famous with the 1926 publication of Ernest Hemingway's novel "The Sun Also Rises."
The bulls that take part each morning are invariably killed by matadors in evening bull fights, and their meat is served up in Pamplona's restaurants.
Dozens of people are injured each year in the "encierros," as the runs are called in Spanish. Most get hurt after tripping and falling in the rush.
The fighting bulls used in the centuries-old fiesta can weigh up to at 1,380 pounds (625 kilograms) and have killed 15 people since record-keeping began in 1924.
Ciaran Giles contributed to this report from Madrid.