China says the "Dalai Lama clique" was responsible for the disturbances in Tibet and protests over the Olympic torch, which reached the top of Mount Everest on Thursday.
The Chinese state-run media this week accused the Tibetan spiritual leader of trying to blacken China's name and prevent its rise, days after the two sides held talks.
Analysts say this conflicting stand of China of maintaining a hardline public face at the same time as offering talks was a common practice.
Lodi Gyari said the Tibetan side had categorically rejected the Chinese accusations the Dalai Lama was behind demonstrations and unrest in Tibet which began in March.
Instead the team of two envoys had argued that events in Tibet were "a clear symptom of deeply felt grievances and resentment of the Tibetans" towards Chinese government policies going back decades.
"The task at hand is to address the legitimate concerns of the Tibetan people in a realistic and constructive way," Lodi Gyari said.
"Despite major differences on important issues, both sides demonstrated a willingness to seek common approaches in addressing the issues at hand," he said.
He said the Tibetan side had appealed for an end to "the current repression" throughout Tibet, the release of prisoners and proper medical treatment for those injured in the recent unrest.
"We welcome the recent statement of President Hu Jintao that his government is 'serious' about the dialogue and his acknowledging that His Holiness the Dalai Lama is being 'conscientious and serious'," he said.
The envoy also called for an end to China's "patriotic re-education" campaign, which he said was deeply resented by the Tibetan people.
On Thursday climbers wearing red brought the Olympic flame to the summit of Mount Everest, unfurling the Chinese national flag, the Olympic flag and a flag bearing the Beijing Olympic logo, and shouting joyously into a TV camera.
But Tibetan groups said they planned prayer vigils around the world later in the day to mourn those killed in protests in Tibet.
The case was shifted from Madurai to Chittoor last year following a Supreme Court directive in response to a petition by two of the relatives of Kiruttinan, saying they would not get a fair trial.
Azhagiri and 12 of his associates were accused of murdering Kiruttinan on May 20, 2003 following a factional feud. Azhagiri was arrested two days later and lodged in Tiruchi central prison. He was later released on bail.