As Singh's birthday falls tomorrow both the leaders cut a cake at the premises of Tsuglagkhang (the main Tibetan temple at Mecleodganj).
The celebrations are going on ahead of the Lama's birthday, which is on July 6, as he is expected to be in the US.
On the occasion, the chief minister referred the Lama as an "apostle of peace and struggle".
Singh, who will turn 81 on Tuesday, released a 10-volume biographical series on the Dalai Lama's life jointly with the spiritual leader.
Also Read
"The Dalai Lama has consistently advocated policies of non-violence, even in the face of extreme aggression and carried out his humanitarian efforts. He became the first Nobel laureate to be recognised for his concern for global environmental problems too," he said.
The chief minister accompanied the Dalai Lama to an exhibition of biographical 'thangka' paintings, depicting the life of the Tibetan monk.
Thousands of Tibetan exiles, foreigners and Indian dignitaries joined in the birthday celebrations here on Sunday too.