Police released a sketch and video of their main suspect, who has been described as foreign and is believed to have been working as part of a network.
The reward for the wanted man now stands at three million baht ($84,000; £53,600).
In his weekly address to the nation, Prime Minister Prayuth said he would "expedite all investigations to bring perpetrators to justice".
The attack aimed to "discredit the government and create a climate of fear to deter tourists," said the Thai police chief, Somyot Poompanmoung.
He also played down his earlier suggestion that as many as 10 people might have been involved.