China, host of the 2008 Olympic Games, on Tuesday condemned the protests as "despicable" but said the flame had not been extinguished.
Jiang Yu, a Chinese foreign ministry spokeswoman, strongly condemned "the deliberate disruption of the Olympic torch relay by Tibetan separatist forces [without regard for] the Olympic spirit and the law of Britain and France".
"Their despicable activities tarnish the lofty Olympic spirit and challenge all the people loving the Olympic Games around the world," she said.
But Jiang said news reports that the security detail protecting the torch extinguished it several times along the route and retreated to the safety of a bus were wrong.
"The reports by foreign media are false in claiming that the Olympic torch was forced to be extinguished during its relay in Paris," she said.
"To protect the security and dignity of the Olympic torch under the circumstances there, the modes of relay were temporarily changed," she said.
Modern tradition of torch relay began in 1936 at Berlin Olympics
This year's is the longest ever, travelling 137,000km
The torch will visit 19 nations over 130 days
First destination is Kazakhstan
On the final leg, it will travel throughout China, including Tibet and the summit of Mount Everest
Click here to go to the official torch relay site
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Despite Monday's protests in Paris and Sunday's in London, Wang Hui, the Beijing organising committee's director of media and communications said "the smooth progress of the torch relay cannot be stopped and will definitely be a big success".
Al Jazeera's Tony Cheng reporting in Beijing said Chinese organisers were due to meet Olympic officials over the protests but the demonstrations were unlikely to change China's policy on Tibet.
Scenes of crowds chanting in Paris with occasional scuffles were reminiscent of the protests that hit the torch's chaotic journey through London on Sunday.
The Paris relay hit trouble shortly after setting off from the Eiffel Tower despite the imposing security cordon thrown around the athletes carrying the flame.
"The Olympic flame is a symbol of peace, of respect and of solidarity. Olympic values were a bit ridiculed today," Bernard Laporte, France's sports minister, told France 2 television. "It's not very good for the image of France."
France's interior ministry said 18 protesters were detained.
Al Jazeera's Tim Friend reporting in Paris said even legislators were chanting "Free Tibet" in France's parliament.
Chinese organisers also cancelled a reception for the torch at Paris city hall at the last minute after protesters hung a banner supporting human rights on the building's facade.
In the US, similar protests are already being staged in San Francisco even before the torch arrives on Wednesday.
|Protesters hung a Tibet flag and banner on|
the Golden Gate Bridge [GALLO/GETTY]
Police arrested three pro-Tibet demonstrators who tied themselves together and scaled the cables of the landmark Golden Gate bridge carrying a Tibetan flag and protest banners.
Even Hillary Clinton, the US Democratic presidential candidate, has joined the fray, calling on George Bush, the US president, to boycott the opening ceremony of the Beijing Games in August to underscore US concerns about the recent unrest in Tibet and questions about China's relationship with Sudan.
Bush has said he will attend the ceremony because the Olympics is a sporting event and not a political one.
The International Olympic Committee chief has urged Beijing to find a peaceful resolution to the Tibet crisis.
Jacques Rogge said he was very concerned "with the international situation and what's happened in Tibet".
"Violence for whatever reason is not compatible with the values of the torch relay and the Olympic Games," he told the Association of National Olympic Committees in Beijing.
Last month Buddhist monks staged protests in Tibet's capital, Lhasa, against Chinese rule which later turned into riots that the Chinese authorities put down, leaving many dead.