Speaking on Israel Radio, Public Security Minister Yitzhak Aharonovitch did not mention Iran explicitly, but strongly implied Israel would seek revenge.
"We know who carried out the terror attacks, we know who sent them, and Israel will settle the score with them," he said.
Thai security forces found more explosives in the house where the Iranian man was staying with two compatriots in Bangkok, but the possible targets were not immediately known, Police Gen. Pansiri Prapawat said. One of the other men was arrested later at the airport.
Monday's attacks appeared to mirror the recent "sticky bomb" killings of Iranian nuclear scientists that Tehran has blamed on Israel.
Israeli police raised their state of alert throughout the country, and officials predicted the attacks were the first in a wave of assaults on Israeli targets worldwide by Iran and its Lebanese proxy, Hezbollah.
The bombings have ratcheted already high tensions over Iran's nuclear program. Israel doesn't believe Iran's claims that it aims to produce electricity, not bombs, and its threats of a possible military strike have grown more ominous in recent weeks.
In Thailand, Tuesday's bizarre sequence of explosions began when explosives apparently detonated by accident, blowing off part of the roof of the Bangkok house.
City surveillance footage from just after that blast showed separate images of each of the suspects walking down the middle of a residential street. One man wearing a baseball cap and a dark jacket carried a large backpack over one shoulder and what appeared to be two portable transistor radios — one in each hand.
A second suspect wearing sunglasses, a T-shirt, pants and tennis shoes also carried a backpack, while the third, dressed in camouflage shorts carried nothing.
A passport found at one blast scene identified one man as Saeid Moradi from Iran, Pansiri said.
Moradi tried to wave down a taxi "but the driver refused," Pansiri said. Moradi then threw an explosive that hit the taxi and partially destroyed it.
Police responding to the first blast tried to apprehend Moradi, who hurled a grenade at them to defend himself. "But somehow it bounced back" and blew off one of legs, Pansiri said.
Photos showed the wounded man covered in dark soot on a sidewalk strewn with broken glass. He lay in front of a Thai school, head raised as if he was attempting to sit up or look around. Hospital officials said Moradi's right leg was severed below the knee, while his left leg was intact but severely wounded.
Later Tuesday night, security forces at a Bangkok airport detained an Iranian — identified as Mohummad Hazaei — as he tried to board a flight for Malaysia, police said. They said he was one of the three in the house where explosives first went off.
A third Iranian is on the run, police said.
Thai government spokeswoman Thitima Chaisaeng said "we need more analysis" to determine who was behind the attack and whether Iran was involved. She refused to comment on what the Iranian suspects might have been planning or whether targets had been identified in Bangkok.
Speaking in Singapore, Barak said Iran and its Lebanese ally Hezbollah are "unrelenting terror elements endangering the stability of the region and endangering the stability of the world."
In India, investigators were searching for what they called a well-trained motorcycle assailant who stuck a magnet bomb on an Israeli diplomatic car in New Delhi, wounding four people Monday.
In Thailand, Prime Minister Yingluck Shinawatra called on people "not to panic" after Tuesday's explosions and said the situation was under control.
The blasts Tuesday wounded three Thai men and one Thai woman, according to Suwinai Busarakamwong, a doctor at Kluaynamthai Hospital.
Last month, a Lebanese-Swedish man with alleged links to pro-Iranian Hezbollah militants was detained by Thai police. He led authorities to a warehouse filled with more than 8,800 pounds of urea fertilizer and several gallons of liquid ammonium nitrate.
Israel and the United States at the time warned their citizens to be alert in the capital.
Pansiri, the Thai police officer, said that "so far, we haven't found any links between these two cases." Immigration police are trying to trace Moradi's movements, but initial reports indicated he flew into Thailand from Seoul, South Korea on Feb. 8, Pansiri said. He landed at the southern Thai resort town of Phuket, then stayed in a hotel in Chonburi, a couple hours drive southeast of Bangkok, for several nights.
Pansiri said a bomb disposal unit checked a dark satchel near the spot where Moradi was wounded, and police found Iranian currency, US dollars and Thai money in the bag.
A bomb disposal squad also said two explosive devices were found in the Iranian's damaged home and defused. They said each was made of three or four pounds of C-4 explosives stuffed inside a pair of radios.
National Police Chief Gen. Prewpan Damapong said the bombs were "magnetic and can get stuck to a vehicle. It can harm people, but not areas."
Thailand has rarely been a target for foreign terrorists, although a domestic Muslim insurgency in the country's south has involved bombings of civilian targets.
The blasts in Bangkok, New Delhi and Georgia have raised worry that a fast-escalating proxy war between Iran and Israel might spread. Iran has accused the Israelis of being behind a series of assassinations of nuclear scientists and other sabotage of its nuclear program. Israel, like the West, believes Iran is pursuing nuclear weapons.