Four people, all believed to be Iranian, are suspected of being connected to explosions in Bangkok on Tuesday, Thai police say.
Two are held in the Thai capital while a third man was arrested in Malaysia.
The fourth suspect, a woman, is still at large. Police say she left the country earlier this month.
Thailand's National Security Council (NSC) chief said possible links to blasts targeting Israeli diplomats in India and Georgia were being examined.
Officials believe that the suspects arrested in Bangkok were planning to attack individuals.
Israel's envoy to Thailand said the explosives found in Bangkok were similar to those used in the attacks.
One suspect was injured when one of the devices went off and another was arrested at Bangkok's international airport.
The third suspect managed to board a flight for Kuala Lumpur on Tuesday night, immigration official Lt Gen Wiboon Bangthamai said.
The Thai deputy prime minister has said that the blasts were not an act of terrorism but rather a "minor symbolic act".
Police say the evidence collected so far suggests "similarities" with attacks against Israeli diplomats in India and Georgia earlier this week, but their investigations are continuing.
"From the investigation, we found the type of explosives indicated that the prepared targets were individuals,'' NSC chief Wichean Potephosree told a news conference.
"Based on the equipment and materials we found, they were aimed at individuals and the destruction capacity was not intended for large crowds or big buildings.''
Police also said magnets were found at the rented house. The devices used in Delhi and Georgia were attached to vehicles using magnets.
The two attacks took place on Monday. An Israeli diplomat was injured in the Delhi attack, after a motorcycle rider attached an explosive device to the back door of the car.
Around the same time a bomb beneath an Israeli diplomat's car in Tbilisi, Georgia, was found and defused.
Israel has blamed Iran for the attacks - Tehran has denied any role. A foreign ministry spokesman also denied any role in the Bangkok blasts, AFP reported.
The three small blasts took place in the Ekamai area in central Bangkok on Tuesday afternoon.
Police told the BBC the first explosion happened at a house which the three suspects were believed to have rented for a month.
Two men managed to escape the explosion that severely damaged the house, but a third man who suffered minor injuries tried to hail a taxi. When the taxi refused to stop for him, he threw at least one bomb at it.
There was a third explosion when the same man then attempted to throw another bomb at police, but missed. The man lost his legs when the device blew up.
Four other people were injured in the incident. The US and UK have issued new travel advisories for Thailand in the wake of the blasts.