Thai police said they did not know if the man suspected of planting the bomb was in the country or not, as they asked Interpol for help.
Authorities in Thailand say the two men handed themselves in to police and are now being questioned.
The men, in red and white T-shirts, rose from a bench shortly before the main suspect, in yellow, sat down and left behind his backpack, according to BBC.
No one has claimed responsibility for the Monday evening explosion at the open-air Erawan Shrine which left 20 people dead and more than 120 injured.
“It is a big network”.
At a news conference earlier in the day, national police chief Somyot Poompanmoung expressed uncertainty about the man’s origin.
Distraught relatives of victims of Monday’s deadly bomb attack in Bangkok have claimed the remains of their loved ones at a forensic institute.
A reward of 1 million Thai Baht ($28,000) is being offered for information leading to the suspect’s arrest, he said.
Since a deadly blast in Bangkok on Monday, Thai authorities have been wrapped up in the aftermath of the event, as they investigate the case and work with families of the victims.
The man is shown in CCTV footage dumping a backpack and walking away from the scene of the blast minutes before the explosion.
“We basically sent in the modus operandi (of the suspect) and also the appearance of the suspect we’re looking for”, Pol Lt Col Kissana added.
The shrine – a popular tourist attraction that typifies the kingdom’s unusual blend of Hindu and Buddhist traditions – and its surrounding had already been largely restored.
Some Chinese media reports also reported on suggestions that the attack (link in Chinese) could be revenge for the Uighur repatriation.
On Wednesday, Police spokesperson Prawut Thawornsiri also indicated about the involvement of two other men who were seen in the video footage.
“I am confident that there are Thais involved but I am not saying it is just Thais or that there are foreigners”, he said.
On Thursday Winthai said 67 patients wounded by the blast remained in hospital while a further 56 had now been discharged.
A Singaporean who did not want to be identified but said his mother was killed in the bombing pays respects at the Erawan Shrine at Rajprasong intersection in Bangkok, Thailand, Wednesday, August 19, 2015. No-one was hurt, but the authorities have not ruled out a link between the incidents.