Warning ? Wen Jiabao's broadcast yesterday, criticising the Dali Lama's "clique".
The Dalai Lama later said he would resign from public life if the situation in Tibet got out of control.
For the first time Mr Wen also directly answered the Dalai Lama's claim that the Chinese Government had conducted "a form of cultural genocide".
"Those claims that the Chinese Government is engaged in cultural genocide are nothing but lies," he said.
"There is ample fact and plenty of evidence proving this incident was organised, premeditated, masterminded and incited by the Dalai clique."
Mr Wen did not say what that evidence was, but added that the motive was to "incite the sabotage of the Olympic Games in order to achieve their unspeakable goal".
In Dharamsala, India, the Dalai Lama responded to Mr Wen's accusations by inviting him to sit down and talk about the problem.
"If the Chinese side ? accepts the reality and addresses the Tibetan problem realistically, within a few hours we can solve this problem," he said.
He said he would retire from public life if the conflict got out of control. "If things become out of control then my only option is to completely resign."
However, he said he remained hopeful he would one day be able to return to Tibet. He also said he expressed his wish for protesters in Tibet "to cool down".
His spokesman, Tenzin Taklha, had earlier rejected allegations the spiritual leader had instigated the protests, saying: "This was very spontaneous."
Mr Wen was speaking at a news conference that is an annual event marking the end of the sitting of the National People's Congress, or legislature. The questions on Tibet were raised by CNN and Financial Times reporters. It is understood Chinese authorities were warned of the broad subject matter, but did not vet details of the questions.
The Tibet riots and subsequent security crackdown have been reported but played down in official Chinese media and completely blocked in most other media and websites. Yesterday's unusually frank news conference by Mr Wen was televised live throughout China on both national and regional TV.
For many Chinese it was the first opportunity to learn of the seriousness of the conflict and the intense interest it has generated around the world.
Mr Wen said he was open to talks if the Dalai Lama's actions supported his verbal support for Chinese sovereignty.
"As long as the Dalai recognises that Tibet is an inalienable part of Chinese territory and that Taiwan is an inalienable part of Chinese territory, our door for dialogue with him is wide open," Mr Wen said.
For his part, the Dalai Lama said a resolution to the problems in Tibet was necessary for China to emerge the global leader it deserved to be. "It must have moral authority in order to be a super power. The Chinese people must know that."
Chinese authorities accused rioters of killing 16 "innocent civilians", saying security forces used only "non-lethal" weapons. Tibetan exile groups say that about 100 people were killed in the subsequent police crackdown.
Mr Wen said the authorities had "exercised massive restraint" and "quickly quelled this incident, and protected the rights of Lhasa residents and of people of all ethnic groups in Tibet".
On the streets of Beijing yesterday most Chinese interviewed by the Herald knew nothing of the Tibetan riots or had only seen brief reports. Overwhelmingly they viewed Tibet as a clean, colourful and desirable holiday destination.
Wang Yuzhi, a young woman waiting for a subway train, said she had not heard of any trouble in Tibet and that she wanted to travel there this northern spring.
"They are very warm, hospitable people," she said.
A middle-aged man called Wang Xin said he also planned to tour Lhasa soon. "The Tibetan question is not such a big thing," he said. "I'm not concerned about safety. I'll go with a travel group."
A journalist with the official Xinhua news agency told the Herald Tibet had traditionally been a war-mongering society ruled by tyrannical monks.
Protesters took to the streets of Dharamsala in support of Tibet soon after Mr Wen made his comments.