Radio Free Asia said the two were believed to be among a few Tibetan youths who gathered to protest against Chinese rule outside the temple, and that they appeared to have died in the blaze.
“The security forces arrived immediately and put out the fire and all the tourists in the area were cordoned off from the site,” a witness told the broadcaster.
“Within 15 minutes, the area was cleaned and not a trace of the incident was left.”
Radio Free Asia quoted a source as saying the situation in Lhasa was now “very tense” and the city was filled with police and paramilitary forces.
One Lhasa resident contacted by AFP on Monday also reported an increased police presence in the city, adding officers were carrying out identity checks in the street and the mobile signal was blocked.
However, security authorities in Lhasa contacted by telephone refused to comment on the incident.
“We are not clear about the situation yet. Wait until the media makes an announcement,” said an official who declined to give his name.
More than 30 people have set themselves on fire in China’s Tibetan-inhabited regions since the start of March 2011 in protest at what they say is religious and cultural repression by the Chinese authorities.
Robbie Barnett, a Tibet expert at Columbia University in New York, said Sunday’s incident marked the first protest in Lhasa since anti-Chinese government riots broke out 2008, before spreading to other Tibetan areas.
“This is the first incident of any significance in four years. It’s a big setback for the authorities,” he told AFP by telephone from New York.
“These self-immolations are very troubling for the Chinese because it is a new method of protest that it very hard to prevent.”
Tibetans have long chafed under China’s rule over the vast Tibetan plateau, accusing Beijing of curbing religious freedoms and eroding their culture and language.
The tensions have intensified over the past year, but Beijing insists that Tibetans enjoy religious freedom and have benefited from improved living standards brought on by China’s economic expansion.
Most of the suicide attempts have taken place around the Kirti monastery in China’s southwestern province of Sichuan, which has become a flashpoint for the mounting anger at Chinese domination over Tibet.
The only previous case in Tibet itself was in December, when a former Buddhist monk set himself alight in Changu prefecture shouting anti-Chinese slogans. He was taken to hospital and later died of his injuries.
Chinese media made no mention of the latest immolations. Internet searches for the Chinese name of the temple where they reportedly occurred, Dazhaosi, were blocked in China on Monday.