The banners read "One World One Dream. Free Tibet" and "Free Tibet."
The protesters wore helmets and harnesses as they made their way up the cables running next to the south tower of the famed span. The climb had the group suspended several dozen feet above traffic.
Mary Ziegenbien, a spokeswoman with the California Highway Patrol, said authorities would not try to go get the protesters out of concern for their safety.
"We don't want to put their lives in danger by going and grabbing them off the suspension cables right now," she said.
The torch relay is scheduled for Wednesday in San Francisco, its only North American stop.
Its path around the globe already has been marked by protests against China's policies toward Tibet and Sudan. In Paris, organizers canceled the final leg of the Olympic run after chaotic protests, snuffing out the torch and putting it aboard a bus.
Security officials put the torch on the bus for the last stretch but stopped right outside its destination, a Paris stadium, so a runner could finish the last 15 feet.
At least two activists got within almost an arm's length of the flame before they were grabbed by police. A protester threw water at the torch but failed to extinguish it and was taken away. Officers tackled numerous protesters and carried some away.
The chaos started on the Eiffel Tower's first floor moments after the relay began. Green Party activist Sylvain Garel lunged for the first torchbearer, former hurdler Stephane Diagana, and shouted "Freedom for the Chinese!" Security officials pulled Garel back.
"It is inadmissible that the games are taking place in the world's biggest prison," Garel said later.
The procession continued but a crowd of activists waving Tibetan flags soon interrupted it by confronting the torchbearer on a road along the Seine River. The demonstrators did not appear to get within reach of the torch, but its flame was put out by security officers and put on board a bus to continue part way along the route.
Less than an hour later, the flame was being carried out of a traffic tunnel by a woman athlete in a wheelchair when the procession was halted by activists who booed and chanted "Tibet." Once again, the torch was temporarily extinguished and put on a bus.
The third time, security officials apparently interrupted the procession because they spotted demonstrators ahead. After the torch was put on a bus, protesters threw plastic bottles, cups and pieces of bread at the vehicle and at a male wheelchair-bound athlete.
The torch disappeared back inside the bus a fourth time shortly after a protester approached it with a fire extinguisher near the Louvre art museum. Police grabbed the demonstrator before he could start to spray.
The flame was whisked into a bus again outside the National Assembly, where protesters gathered. A session of parliament was interrupted and a banner on the building read: "Respect for Human Rights in China." City Hall draped its building with a banner reading, "Paris defends human rights around the world."
The Chinese, who have been hoping to use the games as a showpiece for their newfound prosperity and power, have dismissed the protestors as a small group of Tibetan separatists. But this torch-relay fiasco may well unsettle the big Olympic corporate sponsors, reports CBS News correspondent Mark Phillips. The top five alone spent half a billion dollars on the last games and are poised to spend a lot more this time. The risk of being tainted by association with Chinese policy has become a real one for those companies.
"They are trying very hard not to seem like the bad guy and I think a lot of the companies really do sympathize with the cause. But they are really not sure how to go about this because you don't want to tick off the Chinese government," says Judann Pollack, managing editor of Advertising Age.
Other demonstrators scaled the Eiffel Tower and Notre Dame cathedral and hung banners depicting the Olympic rings as handcuffs.
About 3,000 officers were deployed on motorcycles, in jogging gear and with inline roller skates.
A Paris police official, who spoke on condition of anonymity because he was not authorized to speak to media, says at least 28 people have been taken into custody during the protests.
Pro-Tibet advocate Christophe Cunniet said he and around 20 other Tibet advocates were detained after they waved Tibetan flags, threw flyers and tried to block the route. Cunniet said police kicked him, cutting his forehead. "I'm still dazed," he said.
Mireille Ferri, a Green Party official, said she was held by police for two hours because she approached the Eiffel Tower area with a fire extinguisher.
In various locations throughout the city, activists angry about China's human rights record and crackdown on protesters in Tibetan areas carried Tibetan flags and waved signs reading "the flame of shame." Riot police squirted tear gas to break up a sit-in protest by about 300 demonstrators who blocked the torch route.
"The flame shouldn't have come to Paris," said protester Carmen de Santiago, who had "free" painted on one cheek and "Tibet" on the other.
Torchbearer Diagana said he was disappointed to see the protests, though he understood why activists were there.
"Nothing is happening as planned. It's unfortunate," he told France 2 television.
At least one athlete was supportive of demonstrators. Former Olympic champion Marie-Jose Perec told French television: "I think it is very, very good that people have mobilized like that."
Pro-Chinese activists carrying national flags held counter-demonstrations.
"The Olympic Games are about sports. It's not fair to turn them into politics," said Gao Yi, a Chinese second-year doctoral student in Paris in computer sciences.
France's former sports minister, Jean-Francois Lamour, stressed that, though the torch was put out aboard the bus, the Olympic flame itself still burned in the lantern where it is kept overnight and on airplane flights.
"The torch has been extinguished but the flame is still there," he told France Info radio.
Police had hoped to prevent the chaos that marred the relay in London a day earlier. There, policeangry over China's human rights record leading up to the Beijing Olympics Aug. 8-24. One protester tried to grab the torch; another tried to snuff out the flame with what appeared to be a fire extinguisher. Thirty-seven people were arrested.
In Paris, police had drawn up an elaborate plan to try to keep the torch in a safe "bubble." Torchbearers were encircled by several hundred officers. Boats patrolled the Seine River, which slices through the French capital, and a helicopter flew overhead.
About 80 athletes had been scheduled to carry the torch over the 17.4-mile route that started at the Eiffel Tower, headed down the Champs-Elysées toward City Hall, then crossed the Seine before ending at the Charlety track and field stadium.
French President Nicolas Sarkozy has left open the possibility of boycotting the Olympic opening ceremony in Beijing depending on how the situation evolves in Tibet. Foreign Minister Bernard Kouchner said Monday that was still the case.
Activists have been protesting along the torch route since the flame embarked on its 85,000-mile journey from Ancient Olympia in Greece to Beijing.
The round-the-world trip is the longest in Olympic history, and is meant to highlight China's economic and political power. Activists have seized on it as a platform for their causes, angering Beijing.
Beijing organizers criticized London's protesters, saying their actions were a "disgusting" form of sabotage by Tibetan separatists.
"The act of defiance from this small group of people is not popular," said Sun Weide, a spokesman for the Beijing Olympic organizing committee. "It will definitely be criticized by people who love peace and adore the Olympic spirit. Their attempt is doomed to failure."
The torch relay also is expected to face demonstrations in San Francisco, New Delhi and possibly elsewhere on its 21-stop, six-continent tour before arriving in mainland China May 4.