"Carrying China's bloodstained torch through Tibet where we are seeing evidence of discontent would be adding insult to 50 years of injury."
Security officers quickly grabbed the three members of Reporters Sans Frontieres, a media freedom group, and dragged them away.
Greek police had imposed heavy security around the site, which included armed police watching from nearby hills.
The Greek government condemned the disruption of the ceremony saying it was "not at all in keeping with the spirit of the Olympics".
Later, about 10 Tibetan activists, covered in red paint to simulate blood, marched in the town's main street, shouting slogans against Chinese rule in Tibet.
China has been widely criticised for its deadly crackdown on protesters in Tibet in the past two weeks, a region it has occupied and ruled since 1950.
The protests continued in Tibetan areas on Monday.
China's state-run news agency Xinhua said that a police officer was killed during a protest in Garze Tibetan Autonomous Prefecture, which is administratively part of Sichuan Province.
Xinhua said that a group carrying knives attacked the armed police officers.
The Tibet Support Group, a human rights group, said a source in Garze had told them a monk and a farmer were also killed in the unrest.
In Nepal, at least two protests were broken up by security forces and about 475 people arrested, the UN human rights office in the the country said.
The torch relay began its journey to Beijing with Alexandros Nikolaidis, a Greek taekwondo athlete, who received the sacred flame from an actress representing an ancient Greek high priestess in the ancient stadium of Olympia.
The torch relay will travel 137,000km over 130 days through five continents before reaching Beijing's Olympic stadium for the opening ceremony.
|Dorjee said carrying China's 'bloodstained' |
torch through Tibet would be an insult [AFP]
Earlier, Tibetan exiles had urged the IOC to cancel the torch relay through the troubled region.
Tenzin Dorjee, the deputy director of Students for a Free Tibet, said on Sunday in Olympia: "If the IOC has any respect in itself, the first thing it needs to do is drop the Tibet part of the relay.
The IOC had approved the torch relay that includes Tibet and the peak of Mount Everest.
Rogge said on Sunday that although the IOC was not a political organisation, the games would bring positive change to China.
But Dorjee said: "The IOC has so far not been able to bring more freedom to China.
"I hold Mr Jacques Rogge and the IOC personally responsible for what happens in Tibet."
Andrew Jennings, an investigative journalist and specialist on the politics of international sport, criticised China and how the IOC have handled Beijing's bid.
"There's a very simple answer. If Jacques Rogge and his IOC had any morality or any spine they would uplift the event now from China and take it back to Athens, the facilities are there, or Sydney, Australia. The athletes don't have to pay the price for our consciences," he told Al Jazeera.
|"The IOC didn't care human rights. For a decade they've been talking this nonsense that taking the Olympics to Beijing would bring human rights"|
"The IOC didn't care human rights. For a decade they've been talking this nonsense that taking the Olympics to Beijing would bring human rights. Go and try and say that on the streets of Lhasa, you can't.
"The Chinese have to be told that if they want this event they need to start talking to representatives of the Tibetan people and get the riot police off the streets."
Rogge said he is engaged in "silent diplomacy" with China on Tibet and other human rights issues.
In an interview to the Associated Press news agency on Monday, he reiterated his position that the IOC is not a political organisation and cannot interfere in the internal affairs of China.
But he stressed that he is involved in private dialogue with Chinese leaders and insisted the human rights situation has improved since Beijing got the games seven years ago.
Rogge, who will chair IOC executive board meetings in Beijing next month, said he will then meet Wen Jiabao, the Chinese premier.
"I have a series of points to discuss with him and I'm sure he has points to discuss with me," he said.
The unrest in Tibet began when Buddhist monks demonstrated in Tibet's capital, Lhasa, on March 10, the 49th anniversary of a failed uprising against Chinese rule, and on subsequent days.
Five days later anti-Chinese rioting shook the city and then spread to nearby Chinese provinces with large ethnic Tibetan populations.
Source: Al Jazeera and agencies