Condoleezza Rice, the US Secretary of State, has called on China to open talks with Tibet’s exiled spiritual leader, the Dalai Lama, after an eruption of violence in the region.

Dr Rice issued the call as she flew to Moscow for bilateral security talks and a meeting with Dmitry Medvedev, Russia's president-elect.

“We have really urged the Chinese over several years to find a way to talk with the Dalai Lama, who is a figure of authority, who is not a separatist, and to find a way to engage him and bring his moral weight to a more sustainable and better solution of the Tibet issue,” Dr Rice told reporters aboard her plane.

“I would hope they still find a way to do that,” she said, referring to the current crisis in Tibet, where rioters have been given a midnight (1600GMT) deadline to surrender to Chinese authorities. “There has been a kind of missed opportunity here for the Chinese to engage the moral authority of the Tibetan people.”

But Dr Rice's hosts made clear that they do not share her sentiments. The Russian foreign ministry said that China's relations with the Dalai Lama were “an internal matter” for Beijing.

“Russia has often stated that Tibet is an integral part of China and it considers relations with the Dalai Lama an internal matter for China,” the ministry said in a statement. “Attempts at politicising the holding of the 2008 Olympic Games in China are unacceptable.”

Meanwhile, India pressed its neighbour to find a “non-violent” solution to the unrest in Tibet as opposition MPs stormed out of parliament at the weakness of New Delhi’s response.

“We are distressed by reports of the unsettled situation and violence in Lhasa and by the deaths of innocent people,” Pranab Mukherjee, the Foreign Minister, told the Indian parliament during a debate on the Tibetan crisis.

“We hope all those involved will work to improve the situation and remove the causes of such trouble in Tibet, which is an autonomous region of China, through dialogue and non-violent means,” he said.

The appeal came as Tibet’s Indian-based prime minister-in-exile said that around 100 people have died in pro-independence unrest in the Chinese-ruled region. The exiled Tibetan said that hundreds had been killed.

China has rejected those estimates, saying today that that Tibetan rioters killed 13 “innocent civilians” during violent protests in Lhasa. Officials insisted that no lethal force had been used to quell the rioting.

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