No charges were made against the two men. Their names were withheld, as both had valid work permits and were legal, said sources.
"Everything was found in order by the authorities," sources told PTI.
According to sources, the two men were taken into custody on Sunday night after they were seen on CCTV talking to a foreign suspect wanted in Thailand's deadliest bombing at the Brahma shrine which killed 20 people and injured more than 100 others on August 17.
The police had picked up the two men for questioning as they lived in the room next to one where police had found bomb-making materials.
Indian security agencies too had also checked the background of two men. One belongs to Jammu and Kashmir, while the other is from Karnataka.
So far Bangkok police has issued arrest warrants for 12 suspects. Two have been arrested, both foreigners, one was carrying a Chinese passport.
The first man arrested, Adem Karadak, also known as Bilal Mohammed, has been remanded from military custody to prison.
A suspect arrested near the Cambodia border has been identified as Yusufu Meralli, told military interrogators he had assembled the bomb for the actual bomber, who is yet to be nabbed.
The 25-year-old also identified the mastermind of the attack as one Izaan. He said that Izaan commanded the operation by using the WhatsApp chat application.
Sources say that Meralli has testified that Izaan left Thailand via Suvarnabhumi International Airport on August 16, a day before the bombing, for China and then headed to Bangladesh.