However, he promised leniency for those who "show remorse" and hand themselves in.
"We have been dealing with the incident in accordance with the law," he told a news conference in Beijing on Monday.
"China is a country ruled by law. No country would allow this violence."
He said dozens of people were wounded in the violence in which "people were hacked and burned to death", but the Tibetan governor denied that lethal force had been used against protesters.
"Security forces used great restraint and did not carry or use weapons," the governor said.
"This time a tiny handful of separatists and lawless elements engaged in extreme acts with the goal of generating even more publicity to wreck stability during this crucial period of the Olympic Games - over 18 years of hard-won stability."
With tensions high in Tibet, security was reported to be tight in Lhasa on Monday with police patrolling the streets.
Security forces were also pouring into neighbouring provinces of Gansu and Sichuan to quell protests which have spread to Tibetan communities there.
The AFP news agency said that at least seven Tibetan protesters were shot dead in Sichuan on Sunday during clashes with police.
China has also clamped down on media coverage, barring foreign reporters from Tibet and blocking access to Youtube, as well as many other overseas news websites.
Troops were deployed over the weekend to quell protests in Lhasa, which began on the anniversary of a 1959 uprising against Chinese rule of the region.
Chinese authorities have confirmed that 16 people died in the Tibetan capital but unconfirmed reports from Tibetan exiles in India say the toll was much higher, putting the toll at 80 or more.
China has rejected that number.
On Sunday, the Dalai Lama, Tibet's spiritual leader in exile, called for an international inquiry into what he said was China's "rule of terror" and "cultural genocide" in Tibet.
Speaking from Dharmsala in northern India, he said: "They [the Chinese] simply rely on using force in order to simulate peace, a peace brought by force using a rule of terror."
He stopped short, however, of calling for a boycott of the Beijing Olympic games.
The uprising comes at a sensitive for China, less than 200 days before the games' opening ceremony takes place in Beijing.
The Olympic torch relay which begins shortly is due to pass through the Himalayan region twice.
On Sunday, Jacques Rogge, the International Olympic Committee (IOC) chief, said he was concerned about the Chinese crackdown in Tibet and the neighbouring provinces.
"We are very concerned," he said. "The IOC hopes that there can be an appeasement as soon as possible to this situation, and I also want to offer our condolences to the relatives of the people who lost their lives."
Saying that the IOC was "in favour of the respect of human rights", Rogge rejected the idea of a boycott saying it would only penalise athletes and would not solve anything.
1950 China invades Tibet
1959 Dalai Lama flees to exile in India after failed uprising against Chinese rule
1960s-70s Hundreds of monasteries destroyed during Chinese Cultural Revolution
1965 China announces creation of Tibet Autonomous Region
1989 Dalai Lama awarded Nobel Peace Prize for leading non-violent struggle for Tibet
2006 Opening of first rail line linking Tibet to rest of China
The Chinese organisers of the Olympics have said the Tibetan unrest will not have an impact on the world's biggest sporting event or the torch relay.
Sun Weide, a spokesman for the Beijing Organising Committee of the Olympic Games (BOCOG), said preparations for the torch relay across Mount Everest and Tibet "have been proceeding very smoothly and according to schedule".
He said pro-Tibet groups that were using the games to push their agenda represented only a tiny minority of global opinion.
"We have been receiving tremendous support from the international community for the Olympic Games," he said.
"I think the authorities in Tibet are dealing with the situation and it is now stable."