Deputy Prime Minister Chalerm Yoobamrung said in cooperation with the US, the Thai side found that the they entered the Thai territory recently and were under watch by the Thai side since.
He said the investigation was underway and declined to speculate why the suspects wanted to do the attack in Bangkok.
Chalerm identified the duo as being members of Hezbollah, a Shi'a Muslim militant group based in Lebanon.
He made the statement a couple of hours after the US Embassy in Bangkok issued an urgent alert for its citizens in Bangkok of poosible terrorist attack.
The alert said foreign terrorists may be currently looking to conduct attacks against tourist areas in Bangkok in the near future.
US citizens are urged to exercise caution when visiting public areas where large groups of Western tourists gather in Bangkok.