Thailand has asked Interpol for help in tracking down the man they believe planted a bomb in Bangkok that killed 20 people, sending the international police organisation an image of the suspected bomber.

The military government was initially reluctant in asking for outside help in the investigation of the blast at a famous shrine on Monday evening that killed 20 people and wounded scores.

"We sent a request for assistance," deputy national police spokesman Kissana Phathancharoen told Reuters.

There has been no claim of responsibility and police have not determined a motive for the worst ever bomb attack in Thailand.

Police suspect the young man caught in grainy footage leaving a backpack at the crowded shrine shortly before the explosion is foreign but Kissana said Thai police were not focused on any particular country or region with their appeal to Interpol.

"We basically sent in the modus operandi (of the suspect) and also the appearance of the suspect we're looking for," Kissana added.

The Erawan shrine at a main city-centre intersection is popular with tourists from China and other East Asian countries. About half the victims were foreigners.

The government says the attack was aimed at undermining Thailand's economy.

Prime Minister Prayuth Chan-ocha initially said the attack was Thailand's problem and should be resolved internally.

Police have issued an arrest warrant for an "unidentified foreign man" in a yellow shirt seen in the video footage and have said investigators believe two other men seen on the footage were accomplices.

"We are confident at least three people were involved in this, but maybe more," Kissana said.

Checks at airports and other exit points found that no one matching the description of the main suspect had left the country since the attack, he said.

On Tuesday, a small explosive device was thrown at a busy pier on Bangkok's main river but no-one was hurt. Police have not ruled out a link.

The Erawan shrine, which is popular with Buddhists in Thailand, has since reopened.

Visitors have left messages of condolence, flowers and candles at the site.