Foreign Ministry spokesman Sihasak Phuangketkeow said intelligence reports showed that 10 members of the Pattani United Liberation Organisation, or Pulo, sparked the exodus by spreading rumours in Malaysia about looming violence in southern Thailand.
Prime Minister Thaksin Shinawatra declined to give further details of the accusation at a news conference on Thursday, saying he would let the Foreign Ministry speak for the country.
But he said Thailand would guarantee the safety of the Thai Muslims after they returned home.
It was the first time the Thai government has accused an organisation of being behind the flight of the 131 Thai Muslims, who left Narathiwat province last Monday for northern Malaysia's Kelantan state, where they are being detained.
On the ground, violence continued to stalk southern Thailand. A Thai Muslim villager was gunned down on Thursday by two suspected separatists in the south, police said.
Shot on motorcycle
Sama-ae Jaehwear, 50, was shot by men on a motorcycle as he rode his own motorcycle through his village of Lapae in Narathiwat province along the Malaysian border, police said.
"The victim died while he was being taken to hospital. It's likely that he was shot by militants since he is an ordinary villager and had no personal conflicts with anyone," Colonel Ubon Meeboon, superintendent of the district police station, told AFP.
Critics say the Thai government's
response has been unduly harsh
The UN refugee agency said this week that its officers will interview the Thais, who say they are being persecuted by Thai security forces trying to quell a long-running separatist movement in the largely Muslim south.
Most Thais are Buddhist.
More than 970 people have been killed since January 2004, when rebels unleashed a wave of attacks in the three southernmost provinces of Narathiwat, Pattani and Yala.
Pulo, which counted thousands of fighters in its ranks in the 1970s, was believed to have given up its armed struggle after a government amnesty in the 1980s.
But analysts recently have speculated that diehard members may be orchestrating new attacks in the south.
In a statement released late on Wednesday, Sihasak said the 10 insurgents in Malaysia spread rumours of impending attacks in southern Thailand so that Malaysians would tell their Thai relatives to cross the border and seek shelter.
Sihasak said the separatist group also set up a front organisation called the Patani Malay Human Rights Organisation and a website to alert the UN refugee agency to the 131 Thai Muslims and urge the world body to intervene after the government introduced a new emergency decree in the southern provinces.
Thai PM Thaksin (L) has struggled
to rein in the Muslim insurgency
"Pulo's move was aimed at tarnishing the country's image," Sihasak said.
On its website, www.pmhro.org, the Patani Malay Human Rights Organisation calls itself an "independent, nongovernmental organisation" which "works in Patani Raya, Southern Thailand, and abroad to fight for basic freedoms and peaceful change at the local level".
It says "the people of Patani are constantly being watched and persecuted for crimes not of their doing. This is not the way to solve the insurgency to convince their fellow Malays to give up arms."
It further says Prime Minister "Thaksin must be brought to the Hague for crime against humanity".