Authorities investigating the explosions that brought a busy central city street to a standstill said the men they arrested are believed to be Iranians, a Bangkok Post newspaper report said.
National police chief Priewpan Damapong said foreigners were going to be the targets of their bombs. But a series of mistakes and panic by the suspects meant they fled the house that they were renting.
One of the suspects had both his legs blown off by a bomb blast, police said, giving no further details of their identities, the Post report said.
The chain of events began at the rented house in the Ekamai district at around 2:40 p.m. when an explosion drove the three men outside, police told the BBC.
Police arrested one of the three men and two fled. One of the men who ran away tried to hail a taxi. But when the taxi didn't stop he threw a bomb at it, which went off.
The suspect ran to the next street and stopped in front of a school where he allegedly threw another bomb at a police vehicle. But the explosives bounced off a passing car and exploded in front of him, blowing off his legs, the Post reported.
The injured suspect, believed to be 28 years old, is in serious condition in a hospital. Three passers-by -- aged 33, 62 and 80 -- were injured in the last explosion, the Post report said.
Immigration police chief Wibul Bangthamai told the Post security was increased at all Thai airports after one of the suspected bombers was arrested trying to board a plane several hours after the explosions.
The man reportedly holds an Iranian passport, Metropolitan Police chief Winai Thongsong said. That suspect was about to board an Air Asia flight to Malaysia, the report said.
Police says the three suspects -- one of them still on the run -- arrived in Phuket from Malaysia early this month.
A search of the house found reportedly uncovered around 20 pounds of C4 explosives packed into radios, police said.
The Thai blasts happened only hours after Israel blamed Iran for bombing incidents against Israeli Embassy officials in Georgia and India.
The wife of an Israeli diplomat in New Delhi suffered shrapnel wounds and three other people were injured when the embassy car in which she was traveling exploded.
Police managed to diffuse a bomb on the underside of an embassy car in the Georgian capital Tbilisi.
"Iran is behind these attacks and it is the largest terror exporter in the world," Israeli Prime Minister Binyamin Netanyahu said.
An analyst with the independent security think tank Royal United Services Institute, in London, said the attacks against Israel could usher in a new covert war between Iran and Israel.
The Tbilisi and Delhi attacks came a day after the fourth anniversary of the assassination of Hezbollah leader Imad Mughniyah, a death the organization blames on Israel.
"It has led many to speculate that Iranian perfidy lay behind this brazen and dangerous move," said Michael Stephens, a RUSI researcher.
"The Israeli response has been unusually swift and certain."
"Within an hour Israel's Foreign Minister Avigdor Lieberman stated, 'We know exactly who is responsible for the attack and who planned it and we're not going to take it lying down'."
However, rather than large-scale offensive, increased tit-for-tat attacks is more likely, Stephens said.