Thai police released a sketch of the suspect and asked Interpol for help in hunting a man they said was a "foreigner" who was seen in CCTV footage planting the bomb at the Erawan Hindu shrine that killed 20 people and injured 120 others.
They suspect he had at least 10 accomplices, revised from two.
The labelling swung the focus of investigations on to international terror organisations and links.
But on Thursday a junta spokesman said it was "unlikely" the bombing was the work of international terrorists.
Tourism accounts of 10 per cent of Thailand's economy and an expected one million Chinese had been expected in the country in the next 12 months.
However, police are investigating one possibility the perpetrators were radicalised south-east Asians who had fought with Islamic State in Iraq and Syria and returned to the region with knowledge of how to plant a sophisticated bomb packed with TNT and ball bearings like the one that exploded at the shrine in central Bangkok.
They have formed their own company within Islamic State called Katibah Nusantara, with some experts putting their strength as high as 600.
The organisation has identified countries in south-east Asia for attack and has been connecting local extremist networks, according to Jasminder Singh who wrote a recent report for Singapore's S. Rajaratnam School of International Studies.
Malaysian authorities say militants linked to Islamic State came close to carrying out attacks in Malaysia twice in the past year.
"They are starting to trickle back into the region," said Zachary Abuza, principal of Southeast Asia Analytics, an independent consultancy on south-east Asian politics and security affairs.
But like other possible scenarios on who could be foreign perpetrators, any motive for Islamic State wanting to carry out an attack is not clear.
Islamic State usually claims responsibility for its attacks but no-one has claimed to have carried out Monday's bombing.
Thailand has not joined the international coalition fighting Islamic State and the country maintains a low profile in the Middle East.
"I can't think of a reason why Islamic State would want to hit Bangkok," Professor Abuza said.
Angel Rabasa, an expert on Islamic militancy at the Rand Corporation, said the attack could be the work of Islamic State, which has been expanding its reach into south-east Asia, or an al-Qaeda-related or independent jihadist group.
But he also was puzzled why these groups would not claim responsibility.
Professor Abuza said developments among insurgents in southern Thailand were troubling as radical cell members had become increasingly attracted to Islamic State's ideology and propaganda.
The insurgents were behind the bombing of a car park on the Thai resort island of Samui in July but they have rarely in the past ventured out of their four provinces.
"Although there is no evidence of any Islamic State link to the insurgency, some of the more radical cell members who have already operated beyond the chain of command might look to Islamic State and ask, why have they been so successful? Is it because they are less cautious and more violent?" he said.
Michael Vatikiotis, Asia regional director for the conflict resolution organisation Centre for Humanitarian Dialogue, said a worst imaginable scenario would be that an external jihadist group have linked up with sympathetic elements in Thailand, possibly southern militants, to plan and execute a spectacular terrorist attack.
Thailand's Prime Minister, Prayuth Chan-ocha, has played down the possibility of revenge attack by Uighur Muslims angry at Thailand deporting 109 Uighur men to China in July, which Thai media reported was a key focus of early investigations.
"If they had done it they would have come out and declared their responsibility by now," he said.
Experts said another possible scenario involving foreigners could be Hezbollah, the Shi'a Islamic militant group based in Lebanon.
Three Iranian men linked to the group targeted Bangkok in 2013 when a bomb exploded in a safe house.
But Professor Abuza said the involvement of Hezbollah "makes no sense as they seem to get activated by Iran when the country wants to up the ante".
"That simply does not apply now. Just the opposite," he said.
Thailand's military has hinted that people tossed out of power after last year's coup may be behind the attack.
But hitting a religious shrine and causing mass casualties seems highly counter-productive to their cause, giving the military and its supporters greater cause to crack down and cling to power.
Some anti-military activists have taken to social media to blame the military, saying soldiers wanted to justify their refusal to set a date for elections and to sheet blame for the attack home to its opponents.
But Mr Vatikiotis said the attack had seriously dented the confidence of the military government, which had pinned its tenuous legitimacy on restoring peace and order.
Security experts, including several with knowledge of the Thai investigation, said nothing was certain at this stage.
Foreign intelligence agencies appear to have no information to help point the investigators in any specific direction.
Mr Vatikiotis said a larger question was whether the ugly face of the jihad in Syria and Iraq was starting to wash back to the region.
"Thailand's borders are not impregnable, visas are for the most part not required and Bangkok's seedy underbelly harbors sizeable Arab, African and south Asian communities," he said.
"It would not be hard to develop a cell or activate a lone wolf terrorist."
*Thai police have said a yellow-shirted suspect caught on CCTV footage planting Monday's bomb was heard speaking English and another language and that his appearance suggested he might be from Europe or the Middle East.
They said investigators were convinced two other men seen in the grainy video at the blast site were accomplices.