Earlier this week 500 monks from the Drepung monastery staged a march in the capital, followed by protests of monks at the Lhasa-area Sera and Ganden monasteries.
On Thursday Chinese government officials confirmed reports of protests in Lhasa but said the situation had been "stabilised".
Tibet's spiritual leader, the Dalai Lama, fled into exile in India after the uprising in 1959, nine years after the invasion of Chinese troops.
This week marks the 49th anniversary of the failed uprising, with protests being held in major Asian capitals.
Many Tibetans - including those who say they do not want full independence - are angry at what they see as they supression of their culture amid a surge of migrants from the rest of China.
|Tibetan exiles held protest|
marches in Tokyo [EPA]
The latest show of Tibetan defiance is likely to worry China's leadership as it seeks to secure a stable environment for the Olympic Games to be hosted in Beijing beginning August 8.
The London-based International Campaign for Tibet said that with tensions growing monks at the Sera monastery in Lhasa had gone on hunger strike while protests were reportedly spreading to two remote rural monasteries within Tibet.
"There is an intensifying atmosphere of fear and tension in Lhasa at the moment," Kate Saunders, a spokeswoman told AFP citing witness reports from the Tibetan capital.
She said the initial Chinese response had been more muted than in the past although authorities have detained a number of Tibetans and begun questioning individual monks.
"There are indications that the authorities have begun a process of investigation in monasteries that could lead to detention and torture," she said.
According to Washington-based Radio Free Asia (RFA), monks from Sera are demanding the withdrawal of Chinese paramilitary force from the monastery compound and the release of monks detained earlier this week.
|Indian authorities detained Tibetan protesters|
outside the Chinese embassy [Reuters]
The US-government funded RFA also reported that two monks from another monastery were in critical condition after attempting suicide by slitting their wrists.
But a spokesman for the Tibet Autonomous Region - as it is officially known in China - denied all the claims.
He said there were no arrests or troops surrounding the monasteries, adding that protests had not spread to rural Tibet and that the monasteries were open to tourists.
Rights groups say this week's demonstrations were the biggest protests in Tibet since Chinese authorities declared martial law to quell a wave of pro-independence demonstrations by monks in 1989.
In a statement, the New York-based Human Rights Watch called on China, as well as Nepal and India, which have seen similar demonstrations, to release detained Tibetans.
Sophie Richardson, the group's Asia advocacy director, said: "Peaceful demonstrations are protected under international and domestic laws and they should be permitted, not violently dispersed."