The first blast in Bangkok ripped off part of the roof of an explosives-filled house where the three Iranians were staying, police said.
Surveillance video from just after that blast showed separate images of each of the three suspects walking down the middle of a residential street.
One man — identified by police as Saeid Moradi — could be seen wearing a baseball cap and a dark jacket. He carried a large backpack over one shoulder and what appeared to be two portable transistor radios — one in each hand.
"He tried to wave down a taxi ... and the driver refused to take him," Police Gen. Pansiri Prapawat said. Moradi responded by hurling an explosive device — possibly a grenade — that partially destroyed the taxi and wounded its driver.
Police then tried to apprehend Moradi on a nearby street. He hurled a grenade at them, "but somehow it bounced back" and blew off his leg, Pansiri said.
Photos of Moradi showed him lying on a sidewalk strewn with broken glass in front of a primary and secondary school. Hospital officials said his right leg was sheared off below the knee, while his left leg was severely mangled.
Police said a second Iranian, Mohummad Hazaei, was detained at Bangkok's international airport; he had been seen in the closed-circuit TV video also carrying a large backpack. He wore sunglasses, a T-shirt, pants and tennis shoes.
The third Iranian, dressed in camouflage shorts, carried nothing.
Three Thai men and one Thai woman were wounded and treated at a hospital, said Dr. Suwinai Busarakamwong.
Authorities are trying to trace Moradi's movements. Initial reports indicated he arrived in Thailand from Seoul, South Korea on Feb. 8, Pansiri said, landing at the southern resort of Phuket, and staying several nights in a hotel in Chonburi, a couple hours drive southeast of Bangkok.
A bomb disposal unit checked a dark backpack near the spot where Moradi fell and police found Iranian currency, U.S. dollars and Thai money, Pansiri said.
Prime Minister Yingluck Shinawatra called on people "not to panic" and said the situation was under control.
The U.S. condemned the blasts. State Department spokeswoman Victoria Nuland didn't blame Iran directly, but noted Monday's incidents in India and Georgia, and recent "Iranian-sponsored" and "Hezbollah-linked" plots to attack Israeli and Western interests in Azerbaijan and Thailand.
Will Hartley, head of the Terrorism & Insurgency Center at IHS Jane's in London, said it's "unclear why Iran would risk an attack on Israeli interests in India, when India has been broadly supportive of Iran during the recent nuclear sanctions debate, and is one of Iran's most important trade partners."
"The attacks in India, Georgia and now Thailand have all been highly amateurish," he added. "And lack the sophistication that would normally be expected from an operation executed by either Hezbollah or Iran's own external operations wing, the Quds Force."
Defense Secretary Leon Panetta told the Senate Armed Services Committee on Tuesday that the U.S. has common cause with Israel and the international community to ensure that Iran does not develop a nuclear weapon. He said the U.S. and other nations have taken strong steps with sanctions and stressed the importance of keeping the international community together.
But Panetta said he doesn't think Israel has made a decision to launch a military strike on Iran to thwart its nuclear ambitions.
Last month in Thailand, 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 (4,000 kilograms) 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, but Thai authorities said Thailand appeared to have been a staging ground but not the target of any attack.
Pansiri, the senior Thai police officer, said that "so far, we haven't found any links between these two cases."
Thailand has rarely been a target for international terrorists, but its main airport is a major hub for Asian air travel and its government — heavily reliant on tourism — is tolerant of foreigners and is often accused of corruption and graft.
Since 2004, it has faced domestic Muslim insurgency, but violence has traditionally been limited to the country's three southernmost provinces.
In New Delhi, Indian investigators were scanning closed-circuit TV video in their search for the motorcyclist who stuck the bomb to the Israeli Embassy car that injured four people, including a diplomat's wife. She was in critical but stable condition.
Indian Home Minister Palaniappan Chidambaram said it appeared to be a terrorist attack carried out by a "very well-trained person."
Israeli media reported that Mossad teams are in Bangkok and New Delhi to investigate the explosions.
Associated Press writers Jocelyn Gecker in Bangkok, Bradley Klapper in Washington, Ravi Nessman in New Delhi, and Amy Teibel and Ian Deitch in Jerusalem contributed to this report.
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