UN Secretary General Ban Ki-moon has called on both Chinese forces and demonstrators in Tibet to show restraint after days of rioting.
Mr Ban urged "a peaceful resolution", but made it clear there were no plans for UN intervention.
Up to 80 protesters are reported to have died in the Chinese crackdown.
A Chinese deadline for protesters to surrender has passed, but large numbers of police are patrolling the streets of the regional capital, Lhasa.
Pro-Tibet activists have been demonstrating outside Chinese embassies across the world.
Speaking to reporters in New York, Mr Ban said he had met the Chinese ambassador to express his concern.
China says Tibet was always part of its territory
Tibet enjoyed long periods of autonomy before 20th century
1950: China launched a military assault
Opposition to Chinese rule led to a bloody uprising in 1959
Tibet's spiritual leader the Dalai Lama fled to India
He also had an informal lunch with members of the Security Council, where the issue of Tibet was not on the agenda.
Mr Ban said his office would continuously monitor events inside Tibet but there was no room for intervention or further action by UN officials.
Russia's UN Ambassador, Vitaly Churkin, said Tibet was "not a matter for the Security Council".
His country - a veto-wielding permanent member like China - is chairing the council this month.
UN spokeswoman Michele Montas said on Monday that the body had no independent reports of what was happening in Tibet.
"We have completely conflicting numbers in terms of how many people died," she added.
The exiled Tibetan government says at least 80 protesters died in a Chinese crackdown beginning last week.
The Beijing-backed Tibetan regional government has confirmed the deaths of 13 "innocent civilians", blaming them on mobs in Lhasa, and insists security forces have not used lethal weapons against any protesters.
With China continuing to ban all foreigners from getting into Tibet, the BBC's James Reynolds has been visiting neighbouring provinces where half the Tibetan people live.
In one major city, our correspondent saw police cars at almost every junction and passed a jeep carrying soldiers with shotguns and camouflaged flak jackets.
China calls the Tibetan protests "deliberate sabotage" and many ordinary Chinese people seem to agree, our correspondent adds.
One man told the BBC he wanted the Communist Party to send the army to Tibet to take control.
Another said that the demonstrations were planned by the Dalai Lama to ruin the Beijing Olympic Games.
US Secretary of State Condoleezza Rice has called on Beijing to open talks with the Dalai Lama, who heads the Tibetan government-in-exile from India.
The UK's Minister for Africa, Asia and the United Nations, Mark Malloch-Brown, warned China risked wrecking its international image as the host of this summer's Olympic Games if the Tibet violence escalated.
"With the Olympics ahead... they really will pay a terrible cost in international public opinion if they're seen to violently crack down on dissidents," he told the BBC.
However, the European Union's 27 sports ministers have dismissed the idea of a boycott over Tibet.
"The only people who are punished in a boycott are athletes," said Pat Hickey, president of the European Olympic Committee.
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.