Deputy national police chief Pansiri Prapawat told reporters that the case was submitted to Bangkok's Criminal Court last week.
Two of the suspects were detained in Thailand in February and charged with causing an illegal explosion while the three others fled overseas.
Thailand is seeking the extradition of one of those suspects from Malaysia, where authorities last month applied for a court's permission to send him back to Bangkok.
"The prosecutor was confident he will be handed over by Malaysia and probably we can slap more charges on this group," Pansiri said.
The two other suspects are believed to have returned to Iran.
Thai police have said that Israeli diplomats were the intended target of the plot.
Israel also blamed Iran over the Bangkok blasts, as well as attacks on its embassy staff in India and Georgia a day earlier.
But Tehran has rejected accusations that it is behind a terror campaign against the Jewish state.
The botched attack in Bangkok came to light after an apparently unintended explosion at a house in the capital on February 14.
One of the suspects -- named as 28-year-old Saeid Moradi -- had his legs blown off as he hurled a bomb at Thai police while fleeing. Another, Mohamad Khazaei, was detained trying to board a flight out of the country.