Police said four people had been detained, a Tibetan woman and three members of the Paris-based group Reporters Without Borders.
"This is a disgrace," said Lampis Nikolaou, a Greek member of the IOC. "I am furious with these people ... who did not respect this site. Whatever their differences with China, they should express them in their own countries."
The protests occurred despite heavy security at Ancient Olympia - birthplace of the games - where more than 1,000 police were deployed.
The three French protesters ran onto the stadium's field while Liu Qi, president of the Beijing Olympics organizing committee and Beijing Communist Party Secretary, was giving a speech. One of the men held a banner showing the Olympic rings as handcuffs.
"If the Olympic flame is sacred, human rights are even more so," the French group said in a statement. "We cannot let the Chinese government seize the Olympic flame, a symbol of peace, without denouncing the dramatic situation of human rights in the country."
Moments later, a Tibetan woman covered herself in red paint and lay in the road in front of a runner carrying the Olympic torch into the village of ancient Olympia, while other protesters chanted "Free Tibet" and "Shame on China."
The protesters came within a few yards of the torchbearer, who ran on the spot for about 10 seconds while police in plain clothes removed the female protester and a man holding up a Tibetan flag.
IOC president Jacques Rogge attended the ceremony, where the sun's rays were used to kindle the flame.
"It's always sad when there are protests. But they were not violent and I think that's the important thing," Rogge told The Associated Press.
The incidents came Rogge told The Associated Press in an interview that he was engaged in "silent diplomacy" with the Chinese but wouldn't intervene in politics to try to change their policies.
"We are discussing on a daily basis with Chinese authorities, including discussing these issues, while strictly respecting the sovereignty of China in its affairs," Rogge said.
The Greek government also denounced the incidents.
Reporters Without Borders identified its detained men as Robert Menard, the group's general secretary, Jean-Francois Juliard and Vincent Brossel.
"They are waiting for the prosecutor," spokeswoman Sanny Dumont told the AP. "They don't know if they will be released or charged. They have not been mistreated at all."
When the stadium incident took place, China state TV cut away to a prerecorded scene, preventing Chinese viewers from seeing the protest. Commentators on Chinese TV never mentioned what took place.
Protests are bound to follow the torch throughout its 136-day, 85,000-mile journey across five continents and 20 countries. China pledged strict security measures to ensure its segment of the relay won't be marred by protests. The route is to end at Beijing stadium on Aug. 8.
Tibetan activists have already said they plan to demonstrate elsewhere on the route.
"Later we will do protests in London and Paris," said Tenzin Dorjee, a member of Students for a Free Tibet who protested in Ancient Olympia.
Tibet's deadly protests started March 10 in the capital of Lhasa on the 49th anniversary of a failed uprising against Chinese rule. The demonstrations turned violent four days later, touching off demonstrations among Tibetans in three neighboring provinces.
Almost 140 people have been killed in demonstrations and a crackdown by China's government since the protests started, the main Tibetan exile group said late Monday.
The Tibetan government-in-exile in the northern Indian city of Dharmsala released a statement giving the names and details of 40 Tibetans killed since the protests started in Lhasa.
It said about 100 others also have been killed. The group's previous overall toll was 99 killed.
Beijing's official death toll from the protests in Lhasa is 22, including civilians killed in rioting and three Tibetan suspects who jumped to their deaths to avoid arrest.
"While we have confirmed information on the death toll from the demonstrations so far, it has been extremely difficult to get the details due to all the restrictions that have been imposed by Chinese authorities," the statement from the Tibetan government-in-exile said.
"As the demonstrations continue to spread vastly to many areas in Tibet, the number of people who have died from the brutal military and police suppression during the peaceful demonstrations is astounding," the statement said.
The riots and protests, the largest and most sustained in almost 20 years, have embarrassed and angered Beijing. They have also drawn attention to the country's human rights record ahead of the Beijing Olympics in August.