Thai border controls will tighten after the discovery of three local cases of the South African COVID-19 variant stemming from illegal border crossings, authorities said on Sunday, as the country grapples to contain its worst coronavirus outbreak yet.

The first local case of the South African variant, known as B.1.351, was detected on May 4 in a 32-year-old Thai man after he was visited by family who entered Thailand from Malaysia through an informal border crossing, the director-general of the disease control department said.

Movement of people has been restricted in the affected district and only two other cases of the South African variant, out of 81 cases, have been detected there since the start of May, Opas Karnkawinpong said.

"The South African variant discovered is similar to those found in Malaysia," Opas said.

While there are concerns the variant may threaten the efficacy of COVID-19 vaccines, Opas said mass inoculations will still be effective in reducing the severity and rate of fatality from the disease.

The Thai government said it will increase manpower, checkpoints and electric surveillance along all land borders and order officials to be tougher on the trafficking of illegal migrants.

Authorities in Bangkok have also prohibited movement of labourers at construction workers' camps after 11 camps were among 30 active clusters in the Thai capital.

The government COVID-19 task force has asked construction companies to take care of their workers by providing food and provisions during this period.

There are around 409 workers camps around Bangkok where city authorities say 62,169 workers live, about half who are migrant labourers.

Movement restrictions have also been imposed on markets and call centres around Bangkok.

Thailand on Sunday reported 3,382 new coronavirus cases and 17 new deaths, bringing the total to 129,500 cases and 776 fatalities since the pandemic started last year.