The only North American leg of the Olympic torch relay has been marked by confusion after the route was diverted to avoid crowds of protesters.
Thousands of pro-Tibet and pro-Beijing demonstrators had gathered in San Francisco, prompting fears of violence.
Officials sent the torch on a new route citing safety concerns. The closing ceremony was also moved to a new site.
There were disruptive protests as the relay passed through Europe. It will end in Beijing, home of the 2008 Games.
Meanwhile, President George W Bush has urged China to "begin a dialogue" with Tibet's exiled spiritual leader, the Dalai Lama.
The US House of Representatives has overwhelmingly passed a motion condemning China's "extreme" response to protests in Tibet.
In San Francisco, a planned waterfront closing ceremony in Justin Herman Plaza was moved because of security fears.
San Francisco Mayor Gavin Newsom told Reuters news agency: "We assessed the situation and felt that we could not secure the torch and protect the protesters and supporters to the degree that we wished."
Instead, a muted closing event took place on a motorway fly-over well away from the planned location, says the BBC's David Willis in San Francisco.
Thousands of spectators had been waiting hours to see the torch pass, but many are likely to have been disappointed after the change of route.
Immediately after the torch was lit, the torchbearers went into a warehouse building on the waterfront.
The torch was then driven to a new starting point about a mile away, where it was handed to two runners away from protesters. They set off surrounded by heavy security.
Pro- and anti-Beijing demonstrators have been mingling on the streets all day, prompting some concerns of violence. Television pictures showed China supporters shoving a Tibet activist.
At least one protester was detained before the relay started.
Hundreds of anti-Beijing protesters rallied in the city on Tuesday, after activists hung banners from the city's famed Golden Gate Bridge on Monday.
Tibet is not the only issue prompting the protests - China's policies towards Sudan, Burma and members of the banned Falun Gong spiritual movement are also being opposed.
Officials in Beijing have condemned the disruption that has accompanied the torch so far - but promised that the procession would continue.
However, correspondents say more trouble could force officials from the International Olympic Committee - set to meet in Beijing on Thursday - to consider calling off the rest of the torch's 136,788 km (85,000-mile) journey.
There have been scuffles between Beijing supporters and opponents
President Bush urged China to open talks with the Dalai Lama, who he called a "peaceful man... who is not for independence, but for the cultural identity of the Tibetans being maintained".
Meanwhile, the president's spokeswoman struck a more hesitant note than she has in the past when asked whether the president would attend the opening ceremonies of the Games.
Dana Perino said it was "extremely premature" to confirm what the president's schedule would be in August.
A spokeswoman for UK Prime Minister Gordon Brown said he would not be attending the opening ceremonies - but had never intended to. He will be at the closing ceremony.
'Looting and arson'
In Washington, meanwhile, the House of Representatives overwhelmingly passed a resolution criticising China's "disproportionate and extreme" response to protests in Tibet.
By 413 votes to one, the House called on China to release Tibetans imprisoned after peacefully demonstrating, and allow international monitors and journalists unfettered access to Tibetan areas of China.
But in a statement before the vote, a spokeswoman for China's foreign ministry accused the resolution's supporters of choosing "to remain silent on the violence involved in beating, smashing up properties, looting and arson in Lhasa - and the Dalai clique who premeditated and organised the criminal act of violence".
The Olympic flame was lit in Greece on 24 March and is being relayed through 20 countries before being carried into the opening ceremony in Beijing on 8 August.
In Paris, the torch had to be extinguished three times, while in London there were 37 arrests.
OLYMPIC TORCH ROUTE
Torch lit in Olympia on 24 March and taken on five-day relay around Greece to Athens
After handover ceremony, it is taken to Beijing on 31 March to begin a journey of 136,800 km (85,000 miles) around the world
Torch arrives in Macau on 3 May. After three-month relay all around China, it arrives in Beijing for opening ceremony on 8 August
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