Six people, including a one-year-old girl and two teachers, were gunned down in separate attacks on a teashop and school in Thailand's insurgency-plagued south on Tuesday, police said.

Gunmen sprayed bullets at villagers as they were having breakfast at a teashop in Narathiwat, one of three southern provinces to have suffered nearly nine years of unrest, killing the child, a 25-year-old woman and two men aged 37 and 70.

Four others were injured in the shooting, including a 10-month-old boy.

"We found 62 bullets fired at the scene," local police chief Captain Boonsak Numad told AFP, adding that at least three people were thought to have been behind the violence.

In a second attack later Tuesday, a headmistress and male teacher were shot and killed as they had lunch in the staff cafeteria of a school in Pattani, the latest attack targeting educators.

Police said the group of at least six gunmen stole a school vehicle to make their getaway.

Hundreds of schools in Pattani and Narathiwat have staged brief closures in recent weeks to protest at the risks facing educators, more than 150 of whom have died in the insurgency.

Militants view the school system as an effort by Bangkok to impose Buddhist culture on the Muslim-majority south. Teachers working in non-religious schools are frequently targeted because they are seen as a symbol of government authority.

Thailand's southern unrest has claimed more than 5,300 lives, both Buddhist and Muslim, since it reignited in 2004, with near-daily bomb or gun attacks.

A report by the International Crisis Group on the violence said on Tuesday that successive governments have "opted to muddle through Southeast Asia's most violent internal conflict".

"As Bangkok dithers, the insurgents are growing bolder and stronger," said Jim Della-Giacoma, Crisis Group's Southeast Asia project director.

"But the violence has evolved at a pace that is starting to challenge the ability of the government to respond on its own terms."

ICG recommended a greater push towards decentralisation and closer engagement with local civil society groups and peace negotiations with insurgents.

It added that the deployment of some 60,000 security forces and an emergency decree "have not achieved any appreciable decline in casualties".

"The government should reverse the militarisation of the Deep South, lift the draconian security laws and end the security forces' impunity, all of which help stimulate the insurgency," the report said.