Thai officials say they believe two suspects arrested in Bangkok after a series of blasts were planning to attack individuals.
Thailand's National Security Council chief said possible links to blasts targeting Israeli diplomats in India and Georgia were being investigated.
Israel's envoy to Thailand said the explosives found in Bangkok were similar to those used in the attacks.
Two suspects arrested on Tuesday are said to be Iranian.
One suspect was injured when one of the devices went off and another was arrested at Bangkok's international airport. A third man is said to be at large.
"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.''
Of possible links to attacks on Israeli diplomats, he said: "We haven't found any links but we are still investigating.''
But Itzhak Shoham, Israeli ambassador to Thailand, was quoted by the Associated Press news agency as saying that the explosives used in the Bangkok blasts were similar to those in India and Georgia.
"From that we can assume that there is the same network of terror," he said.
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.
They come a month after Thailand arrested a Lebanese man with suspected links to Hezbollah, a Lebanon-based Shia Islamist movement backed by Syria and Iran. Police found large quantities of bomb-making materials after the man's detention.
It is not clear if his case is related to this incident.