An international Olympic official also criticised the protests, but said the relay would stay on its round-the-world course.
Officials in Paris on Monday were forced to hustle the Olympic torch on to a bus when protesters against Chinese policy in Tibet tried to seize it.
In London the day before, activists waving Tibetan flags and shouting "Shame on China" also turned the event into a torrid obstacle course.
China quickly condemned the disruptions as "vile" and, in a departure from past reticence, state-run television and newspapers showed the protests and upset spectators.
"We express our strong condemnation of the deliberate disruption of the Olympic torch relay by 'Tibetan independence' separatist forces," Foreign Ministry spokeswoman Jiang Yu said in a statement posted at www.fmprc.gov.cn.
Beijing Olympics spokesman Sun Weide told reporters that the Paris demonstrations were "blasphemy".
The torch relay disruptions follow unrest in Tibet that China has said was the work of the Dalai Lama, the exiled Tibetan Buddhist leader. He has repeatedly denied China's claims.
Beijing's subsequent security drive in Tibet and nearby areas has galvanised international groups denouncing the crackdown and calling for the mountain region's autonomy or independence.
The press chief of the International Olympic Committee, Kevan Gosper, said he was "desperately disappointed" by the chaotic scenes in Paris, which could well be repeated in San Francisco, where the torch heads next.
"When people get to the point where they will break lines, take the torch, try to put the torch out, I think one would argue that does a lot of harm to their own cause," Gosper said.
"My belief is the torch relay will stay on course, there may be adjustments to it but I think it would be wrong to do anything other than try and get the torch through to its ultimate destination."
NATIONAL PRIDE
