The whole world is watching China's reaction to protests in Tibet, UK Prime Minister Gordon Brown has told MPs.
Exiled Tibetans have been holding their own protests in Kathmandu
Mr Brown said the EU had "made our views known" to China and urged "restraint and an end to violence".
Dozens of people are feared dead after days of rioting in the Tibetan capital city of Lhasa.
Conservative leader David Cameron said China had to understand that with the bigger role it was playing in the world came greater responsibility.
Calls for dialogue
China gave demonstrators in the city until midnight (1600 GMT) to give themselves up or face punishment.
Dozens are feared dead after days of rioting, with each side accusing the other of excessive force.
In a Commons statement on last week's EU summit, Mr Brown was asked about the situation in Tibet.
Conservative leader David Cameron said while ministers were meeting in Brussels there had been violence on the streets of Tibet.
"Britain, rightly, works closely with China and we very much welcome the way it has opened up its economy," he said.
"But isn't it vital that the Chinese government understands that with the greater role that it plays in the world, comes greater responsibility?"
He asked Mr Brown: "Do you agree that the strong relationship that we all want with China requires us to be candid and frank - even on issues where we disagree."
Mr Brown said that while the issue had not been discussed at the EU summit, "all of us" were concerned about the situation.
"We have made our views known to the Chinese authority. We believe there should be restraint and an end to violence," he said.
"And we believe there should be a dialogue - and that should happen soon, between the different authorities."
He added: "The whole world, at this time, is looking to China to see what the reaction is."
The disruption comes ahead of the Olympic Games in Beijing this summer.
Labour MP Harry Cohen, chairman of all-party group on Tibet, said: "This is China back to Tiananmen Square in terms of crushing human and democratic rights."
And the Lib Dem vice chairman of the group, Norman Baker, said he feared those who gave themselves up faced torture and long imprisonment, while those who did not would be shot.
But Qiangba Puncog, the Tibetan regional governor, said that 13 "innocent civilians" had been killed by mobs in Lhasa and blamed the unrest on outside forces including Tibet's spiritual leader the Dalai Lama.
"The Dalai group and some other people in Western countries look at the beating, burning and smashing activities in the riots in Lhasa as peaceful demonstrations," he said
"No democratic country in the world will tolerate this kind of crime."
China says Tibet has always been part of its territory. But Tibet enjoyed long periods of autonomy before the 20th Century and many Tibetans remain loyal to the Dalai Lama, who fled in 1959.