Somyot said Tuesday that authorities were looking for a suspect seen on closed-circuit television (CCTV) footage near the shrine.
The suspect was wearing a yellow shirt and could be Thai or a foreigner, he said.
"That man was carrying a backpack and walked past the scene at the time of the incident. But we need to look at the before and after CCTV footage to see if there is a link," Somyot told a news conference.
"Police are not ruling out anything including [Thai] politics and the conflict of ethnic Uighurs who, before this, Thailand sent back to China," Somyot had told reporters earlier.
Thailand forcibly returned 109 Uighurs to China last month. Many of the largely Muslim minority have fled unrest in China's western Xinjiang region, traveling through Southeast Asia to Turkey.
Bangkok will set up a "war room" to coordinate the response to the blast, the Nation television channel quoted Prayuth as saying.
Prawit said the bombers intended to discredit the government and harm the economy.
"We didn't expect this to happen in a crowded area," he says. "They aim to destroy tourism, economy, our country. But during crisis, we can build unity."
"The perpetrators intended to destroy the economy and tourism, because the incident occurred in the heart of the tourism district," Prawit said late Monday.
The Erawan Shrine, dedicated to the Hindu god Brahma, is popular among Thailand's Buddhists as well as Chinese tourists. Three Chinese citizens were among the dead, the official Xinhua news agency said. Two Hong Kong residents, two people from Malaysia and one person from the Philippines were also killed in the blast, officials said. Many of the wounded were from China and Taiwan.
“This probably the worst bomb in the history of Bangkok,” Pravit Rojanaphruk, a political analyst and regular columnist for Thailand's Nation newspaper, told Al Jazeera. “Bangkok itself has no history of a major-scale bomb with mass casualties.”
At least 20 people have been confirmed dead and 117 injured, Thailand's Narinthorn emergency medical rescue center reported on Tuesday.
The power of the blast blew the iron gates outside the shrine outward, and Thai officials said that high-grade explosives were used. Shrapnel from the explosion could be seen as far as 100 yards from the scene, which authorities cordoned off initially to make way for emergency vehicles. Somyot said the blast was caused by a pipe bomb.
Thai forces are fighting a low-level Muslim insurgency in the predominantly Buddhist country's south, but those rebels have rarely launched attacks outside their heartland.
"This does not match with incidents in southern Thailand. The type of bomb used is also not in keeping with the south," Royal Thai Army chief and deputy defense minister General Udomdej Sitabutr said in a televised interview.
"Collection of evidence last night was not complete," Udomdej said.
Tourism is one of the few bright spots in an economy that continues to underperform more than a year after the military seized power in May 2014.
It accounts for about 10 percent of the economy, and the government had expected a record number of visitors this year following a sharp fall in 2014 during months of street protests and the coup.
The country has also been divided for a decade by intense and sometimes violent rivalry between political factions in Bangkok and elsewhere. The country remains tense and deeply divided after nearly a decade of endless protests punctuated by two coups.
Self-exiled former Prime Minister Thaksin Shinawatra sits at the heart of the political divide. His parties have won every election since 2001, but he is disliked by the Bangkok-based elite.