Politicians in India have expressed concern over the Chinese response to protests inside Tibet.
Mr Mukherjee's comments have not pleased some opposition parties
In a debate in the Indian parliament, Foreign Minister Pranab Mukherjee said he was distressed by reports of the violence in the Tibetan capital, Lhasa.
He said that he hoped the troubles would be solved through dialogue and non-violent means.
Meanwhile police in Nepal have dispersed a crowd of 100 Tibetan protestors and Buddhist monks.
Televised pictures showed police beating some of the protesters and detaining dozens of others in the capital, Kathmandu.
"We are distressed by reports of the unsettled situation and violence in Lhasa and by the deaths of innocent people," Mr Mukherjee told the Indian parliament during a debate on Tibet.
"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.
His remarks were criticised by some opposition parties, who described them as an "inadequate response".
Exiled Tibetans have staged several protests in Nepal
"Over 100 innocent protesters have been massacred in Lhasa in the past one week by the Chinese security forces which are involved in ethnic cleansing," Bharatiya National Party MP Vijay Kumar Malhotra said.
"This house should condemn the incidents," Mr Malhotra said.
Mr Mukherjee reiterated that India's policy of non-interference in China was still the same despite recent events.
"New Delhi's policy on China and Tibet has remained unchanged since 1959 despite various political parties being in power at the centre since then," he said as opposition leaders staged a symbolic walkout.
The BBC's Charles Haviland in Kathmandu says that Monday's protest by Tibetans was the first time in a series of demonstrations in Nepal that they have been confronted by police firing teargas.
Our correspondent says that there were running battles between demonstrators and police, with protesters being baton charged and people in the crowd being dragged along the ground.
Several people were injured in scuffles and a monk was seen with blood streaming down his face.