The sketch shows a fair-skinned man with thick, medium-length black hair, a wispy beard and black glasses. It was unclear whether the man was Thai or a foreigner.
On Tuesday, a day after the bombing at a religious shrine in Bangkok's busy Ratchaprasong commercial district, police released grainy closed-circuit television (CCTV) footage of a young man wearing a yellow t-shirt.
The man is shown in CCTV footage dumping a backpack and walking away from the scene of the blast minutes before the explosion.
Police have said the man is a suspect but that others could be behind the attack. They have not ruled out any group, including elements opposed to the military government, though they said it did not match the tactics of Muslim insurgents in the south or 'red shirt' supporters of the previous administration.
The sketch, say police, could help locate the yellow-shirted man seen in the CCTV footage. A one million baht ($28,000) reward has been offered to anyone who can give police information leading to his arrest.
Police also said they would take the sketch to a court and ask that an arrest warrant be issued for a man matching the description.
"We think the investigation team will ask for the arrest warrant tonight," said police spokesman Prawut Thawornsiri.
Police chief Somyot Pumpanmuang told a news conference that it was not clear how many people were involved in the attack or if they were still in the country.
At the same news conference, spokesman Prawut said "two to three" people had been questioned by police since the attack.
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