“We have information that they may have links to the blasts,” Police Major General Piya Utayo told AFP, adding no charges had been brought against the three.
One was detained under immigration law for overstaying his visa. “We are checking the other two people’s backgrounds,” Piya added.
According reports in the Thai press, mobile phone call logs revealed that one of Monday's suspects had been in regular contact with two Iranians now in custody, one of whom blew his own legs off as he hurled a bomb at police while attempting to flee.
The new suspects were picked up in a raid Sunday in an apartment tower in eastern Bangkok.
Another suspect was detained earlier this month in Malaysia, while arrest warrants have been issued for two more Iranians believed to have left the country.
Israel has directly accused Iran and its terror proxy Hizbullah of being behind the Bangkok blasts, as well as attacks on Israeli embassy staff in India and Georgia on February 13.
Tehran has rejected accusations that it is behind a terror campaign against the Jewish state, saying it is "ready to help identify those responsible."
Hizbullah denied culpability in the attacks as well saying they were not sufficiently grandiose for the terror group to carry out, but did not shy away from saying it was targeting Israel in a terror campaign.
Hizbullah chief Sheikh Hassan Nasrallah instead implied the terror group would target senior Israeli officials and not “simple Israelis” like those targeted in Bangkok.
Bangkok has been on alert since mid-January when police arrested a Lebanese man with links to Hizbullah on suspicion he was planning an attack, following a US warning that tourists might be targeted.