The footage, from a security camera, shows a man in a yellow shirt leaving a backpack in the Erawan Hindu shrine.
At least 20 people died in the attack on August 17. About half of the victims were foreigners.
More than other 120 people were injured in the attack.
In a separate attack on August 18, an explosive device was thrown at a pier in Bangkok, but no-one was hurt.
Nationals from China, Hong Kong, the UK, Indonesia, Malaysia and Singapore are among the foreigners killed in Monday’s attack.
Still images of the suspect had already been released.
In the new footage, he is shown carefully and deliberately removing his backpack inside the shrine, getting up without it and immediately leaving the scene.
“There is a suspect… we are looking for this guy,” PM Prayuth Chan-ocha told reporters.
Authorities were “quite close” to identifying the suspect, Thai government spokesman Maj. Gen. Weerachon Sukhontapatipak said.
However, other leads were also being pursued.
The spokesman said no motive was being ruled out, but that the bomber did not appear to be Thai and the character of the bombing was “quite different” from previous bombings by southern Thai insurgents.
He said security at transport hubs and tourist sites was being beefed up.
The bomb was detonated at about 19:00 local time on August 17 when the shrine, and the nearby Ratchaprasong junction, were crowded.
PM Prayuth Chan-ocha called it the “worst ever attack” on Thailand.
“There have been minor bombs or just noise, but this time they aim for innocent lives. They want to destroy our economy, our tourism.”
In Tuesday’s incident, a device – possibly a grenade – was reportedly thrown at the busy Sathorn pier in Bangkok.
It landed in water where it exploded harmlessly, but police said it could have caused many injuries.
Monday’s bomb was clearly placed to cause maximum casualties.
In currency trading, the Thai baht fell to its lowest level in six years over concerns about the impact on tourism.
National police chief Somyot Poompummuang described the device as a 6.6lb pipe bomb – an improvised device where explosive material is put in a sealed cavity to maximize the explosive impact.
Erawan shrine is dedicated to the Hindu god Brahma, but is also visited by thousands of Buddhists each day.
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