The atmosphere between the two men was relaxed
Taiwan's President Chen Shui-bian has thanked Tibet's spiritual leader, the Dalai Lama, for his visit to the island in the face of strong opposition from China.
The views of Chinese leaders should change along with global trends
The Dalai Lama
At a meeting between the two men in Taipei, President Chen said the exiled Tibetan leader had faced pressure from all sides, but had not given in.
The Dalai Lama told the Taiwanese leader that changes in China made him hopeful about the future of Tibet, adding that as the world became more open and democratic, China's leaders should change their ideas.
China has angrily denounced the visit, accusing the Dalai Lama of seeking collaboration between Tibetan activists and what it calls Taiwanese independence forces.
The Dalai Lama has insisted all along that his visit is for religious reasons.
Traditional gift
At their meeting, the Tibetan leader presented President Chen with a silk scarf - a traditional sign of respect.
This has been a visit of largely spiritual concerns
President Chen gave the Dalai Lama a wooden statue.
The BBC's Damian Grammaticas, reporting from Taipei, says it was the most significant and controversial moment in the 10-day visit.
But in deference to China's sensitivities, most of the encounter between the two men took place behind closed doors.
After their one-hour meeting, the Dalai Lama headed to the Linkou Stadium in northern Taoyuan county for another day of Buddhist preaching.
The majority of the five days the Dalai Lama has already spent on the island have been spent in religious teaching.
Chinese suspicions
Our correspondent says China is particularly suspicious of the meeting because President Chen Shui-bian, who was elected as Taiwan's leader last year, comes from a political party that has in the past advocated full independence for the island.
However, the Dalai Lama has insisted he does not want independence for his homeland and he is not seeking any form of alliance with Taiwan.
He has repeatedly said that autonomy for Tibet may be the best solution.
China claims sovereignty over Taiwan, which it sees as a renegade province, and Beijing refuses to talk to the Dalai Lama about autonomy for Tibet.