The blast occurred on Monday in one of the Thai capital's most popular tourism hubs, ripping through a crowd of worshippers at the Hindu shrine close to five-star hotels and upscale shopping malls.
Chinese, Hong Kong, Singaporean, Indonesian and Malaysian citizens were among the 20 people killed, police said.
More than 100 other people were injured as the blast left body parts strewn across crushed pavement, alongside shattered windows and incinerated motorcycles.
Junta chief Prayut Chan-o-cha on Tuesday branded the bombing the "worst ever attack" on Thailand, as he said the hunt was on for a suspicious man filmed on closed circuit television near the shrine.
"Today there is a suspect... we are looking for this guy," Prayut told reporters.
Police released CCTV footage showing the apparently young man in a yellow T-shirt walking near the shrine wearing a backpack, but then a short time later walking away without it.
"Things are becoming clearer now," Defence Minisiter Prawit Wongsuwon told reporters, although he declined to give details and authorities did not reveal if they had any motives for the attack.