Thai PM Prayuth Chan-ocha said progress was being made in the investigation.
A multi-faith memorial to the victims of the attack was held at the shrine on Friday.
Little evidence has emerged from the attack, which Prime Minister Prayuth called Thailand`s worst-ever.
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.
At the Erawan Shrine on Friday, doves were released at a memorial ceremony attended by Buddhist, Muslim, Christian, Hindu and Sikh leaders.
One of the organisers said it was to remember the victims, but also "to tell tourists that we will try to protect you who will be coming here in the future all the best we can".
Various theories abound about what motivated the attack, from internal political unrest to insurgents in the south, although the Thai authorities say it is unlikely to be the work of an international terror group.
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