Thai security forces are sharing information with Interpol, the global police organization, and with intelligence agencies from allied countries, officials said.
At this point, they don't know if the main suspect is still in Thailand, said Prawut, the police spokesman.
He said investigators are reviewing surveillance video from Bangkok's two international airports as well as from the scene of the bombing.
Thai police have released a sketch of the suspect in the shrine bombing.
Police have released a sketch of the suspect, showing a dark-haired man with glasses and light facial hair.
Police on Thursday doubled the reward for information leading to the suspect's arrest to 2 million Thai baht ($56,000), according to the government-run National News Bureau of Thailand. They raised it further Friday to 3 million baht ($84,000), Somyot said.
A Thai motorbike taxi driver who believes he picked up the suspect shortly after the blast said he did not seem to be Thai.
Driver Kasem Pooksuwan told CNN the man didn't speak to him but showed him a piece of paper with the name of a central city park written in English. He spoke an unfamiliar language on his cell phone during the short ride, he said.
"When I dropped him, he still appeared very calm, just like (a) normal customer. He seemed not in a hurry at all," Kasem told CNN.
Police say they have questioned the motorcycle taxi driver but haven't provided details of what he told them.