The military took over on May 22 after months of protests that had undermined the government of Prime Minister Yingluck Shinawatra, forcing ministries to close for weeks on end, hurting business confidence and causing the economy to shrink.
Protests against the coup have taken place in Bangkok most days since then although they have been small and brief.
On Sunday the authorities are anticipating that protesters will gather at several spots in the capital including an area in the centre where big malls are located. The military has banned political gatherings of five people or more.
Deputy police chief Somyot Poompanmoung told Reuters that 5,700 police and soldiers were being sent to these areas and rapid deployment units were ready to stop protests that spring up elsewhere.
Some top-end malls around the Ratchaprasong area have chosen to close or have reduced opening hours, and the operator of the Skytrain overhead rail network has shut several stations in the central area.
"It's a business centre and we need to protectively avoid any damage if authorities need to break up a gathering," Somyot said, adding mall owners could also find themselves in trouble with the authorities if protests took place on their premises.
On Saturday, as on the two previous days, the authorities effectively closed down the normally busy roads around Victory Monument, which was becoming a focal point for opposition to the coup. The area was flooded with police and troops but no protesters turned up.
In a televised address late on Friday, army chief and coup leader General Prayuth Chan-ocha said the military would need time to reconcile Thailand's antagonistic political forces and push through reforms.
He outlined a process beginning with three months of "reconciliation". A temporary constitution would be drawn up and an interim prime minister and cabinet chosen in a second phase, taking about a year, he said. An election would come at an unspecified time after that.
The United States, European Union countries and others have called for rapid restoration of democracy.
At a conference in Singapore on Saturday, U.S. Defence Secretary Chuck Hagel urged the Thai armed forces to release detainees, end censorship and "move immediately to restore power to the people of Thailand, through free and fair elections".
Australia scaled back relations with the Thai military on Saturday and banned coup leaders from travelling there.
At the heart of nearly a decade of political turmoil in Southeast Asia's second-biggest economy is conflict between the Bangkok-based royalist establishment dominated by the military, old-money families and the bureaucracy, and supporters of former telecommunications mogul Thaksin Shinawatra, who is adored by the poor in the north and northeast.
Thaksin, who was ousted as premier in a 2006 coup, is the brother of Yingluck and was considered the real power behind her government. He has chosen to live in exile since fleeing a 2008 conviction for abuse of power.