"The people of Nepal and Tibetans have been neighbours throughout history and many Tibetan refugees live in Nepal. I offer my condolences to you and to those who have lost members of their families, friends and their homes in this tragedy."
He added: "As a token of solidarity with the people of Nepal, I have asked the Dalai Lama Trust to make a donation towards rescue and relief efforts."
The 7.9 Richter scale tremor that struck Nepal on Saturday also affected parts of Tibet. The two border ports to Nepal were seriously affected. Reports indicate that the death toll in Tibet has reached 20.
In addition to the reported deaths, a total of 58 people have been injured, four continue to be missing and 12,000 others evacuated. The quake also toppled 1,191 houses, damaged roads and cut off telecommunications in two counties in Shigaze.
The massive earthquake in Nepal, the worst in over 80 years, has so far claimed over 3,600 lives and left more than 6,000 others injured. Officials have warned that the number of casualties will most likely continue to rise as rescue teams reach remote mountainous regions of western Nepal.
According to reports, rescuers continued to scour Indian villages and towns bordering Nepal as India's death toll reached 62, including 40 in Bihar, with nearly 260 injured.
In Bangladesh, four people died, two of them from heart attacks, when the quake struck, according to a report by the Daily Star.