Thousands of police and soldiers have been deployed around the Thai capital, Bangkok, to try to prevent anti-coup protesters from gathering.
Parts of the city centre have been blocked off to traffic, and train stations are closed.
Activists have been using social media to call for a nationwide protest.
The Thai army seized power on 22 May and detained senior politicians for several days, saying stability had to be restored after months of unrest.
Demonstrations against the coup have taken place almost daily in Bangkok, despite a ban by the military authorities on political gatherings of five or more people.
Bangkok's commercial heart was almost deserted on Sunday, after the army sealed it off to stop what was expected to be a large show of defiance, reports the BBC's Jonathan Head in the city.
Deputy police chief Somyot Poompanmoung told Reuters that 5,700 police and soldiers were being sent to areas of the city, including shopping centres where previous rallies have sprung up.
"It's a business centre and we need to protectively avoid any damage if authorities need to break up a gathering," he said.
The coup leaders have repeatedly warned that they will take tough action against anyone opposing their authority.
So far there have been only minor scuffles between troops and protesters, although a number of alleged protest leaders have been arrested, our correspondent says.
Army chief Gen Prayuth Chan-ocha announced on Friday that elections would not be held for more than a year, to allow time for political reconciliation and reform.
Thailand's military stepped in after six months of political deadlock as protesters tried to oust the government of Prime Minister Yingluck Shinawatra.
At least 28 people were killed and several hundred injured during the unrest.
Since taking power the military has summoned and detained dozens of politicians, including Ms Yingluck, as well as journalists and academics.
The current deadlock dates from 2006, when the military ousted Ms Yingluck's brother, Thaksin Shinawatra, in a coup.
Both have strong support in rural and northern areas, propelling them to successive election wins.
However, many in the middle class and urban elite, who comprise the heart of the anti-government movement that began in November 2013, oppose them bitterly.