"Many points on the human rights group's demands are in line with the commission, which aims to work on long-term peace and reconciliation," said former prime minister Anand Panyarachun, who heads the commission.
The 48-member National Reconciliation Commission, which was meeting late into Friday night, was named last month by Prime Minister Thaksin Shinawatra.
It faces the task of proposing ways to end the insurgency that erupted in January 2004 and has since claimed more than 640 lives.
The insurgents have mounted almost daily attacks in the three southernmost provinces near the Malaysian border - usually small shootings or bombs targeting government officials, including teachers, but also random violence against villagers.
A bomb exploded early on Friday outside the Sukkhirin municipality office in Narathiwat province, slightly injuring a security guard and destroying a pickup truck.
Thailand has imposed drastic new security measures around the country after a triple explosion targeting an airport, a hotel and a supermarket in the southern city of Hat Yai on 3 April killed two people and injured more than 75, sparking fears the insurgents were expanding their operations.
Three explosions killed two
people in south Thailand
Chaturon Chaisang, deputy prime minister, said the Airports Authority of Thailand has agreed to pay one million baht each ($25,200) compensation for those killed in the 3 April blast, and 800,000 baht each to survivors disabled by their injuries.
"For the blast at Carrefour, government agencies will coordinate negotiations between the private company and victims, and the government will assist if any lawsuit is expected," he said, referring to the blast at the hypermarket.
Rights groups have condemned Thaksin's handling of the unrest as heavy-handed, although the prime minister last month made a series of conciliatory gestures, including the naming of the new commission.
An ad hoc coalition of 10 rights groups presented a list of demands to the commission as it began its first meeting at the foreign ministry in Bangkok.
Rights groups say Bangkok has
Among their demands were an end to martial law in three southern provinces, and the release of investigations into two highly controversial clashes last year at the Krue Se mosque on 28 April and during a protest at Tak Bai on 25 October.
The rights groups also called for an investigation into the mysterious disappearance of prominent Muslim lawyer and activist Somchai Nilapaijit, and for the government to review its list of top suspects in the insurgency.
"Some people may have been treated unjustly by government officials," the statement said.
They also called for reducing the heavy police and military presence in the south, which is majority Muslim and ethnic Malay, unlike the rest of predominantly Buddhist Thailand.
Pracha Tarat, Narathiwat governor, separately said relatives of 85 Muslims who died and seven still missing after the Tak Bai protest would begin receiving 300,000 baht compensation each on Saturday from the provincial Islamic office.
Most of the Tak Bai victims suffocated after being tied and piled face-down in army trucks after the protest.