A foreign man described as a "main suspect" in the deadly Bangkok bombing was arrested Tuesday, with Thai police calling him an important figure in the network that staged the attack.

The man detained near the border with Cambodia is the second foreigner held over the August 17 blast at a religious shrine which killed 20 people, mostly ethnic Chinese tourists.

Police also said arrest warrants have been issued for three fresh suspects still at large, two of whom have names which appear foreign.

Prime Minister Prayut Chan-O-Cha said the unidentified foreigner was picked up in Sa Kaeo province on the Thai side of the Cambodian border.

Asked whether he is thought to be the person who planted the bomb at the Erawan shrine in Bangkok's busy Chidlom shopping district, he replied: "We are interrogating. He is a main suspect and a foreigner."

National police spokesman Prawut Thavornsiri said investigators believe the suspect is "an important person in the network" behind the bombing, Thailand's worst single mass-casualty attack.

The man speaks English, Prawut said, adding he appeared "similar" to a prime suspect captured on security camera footage leaving a bag at the scene moments before the blast.

The man was detained around noon trying to cross into Cambodia from the Thai countryside, away from towns or roads.

Footage played on Thai television showed the unnamed suspect, wearing a hat and sunglasses, accompanied by uniformed soldiers.

DNA samples were being taken from the man, the spokesman added, to see if they match any locations searched by police.

Fresh arrest warrants are also out for three new suspects for possessing bomb-making material, Prawut said, holding up an iPad with sketches of the men.

One was unnamed but the other two were identified as Ahmet Bozaglan and Ali Jolan, although Prawut did not give their nationalities.

The motive for the shrine attack remains shrouded in mystery.

Suspicion has fallen intermittently on Thailand's bitter political rivals, organised criminal gangs, Islamist militants, rebels in the kingdom's strife-torn south and sympathisers of refugees from China's Uighur minority.

 As speculation has swirled, a connection with Turkey has repeatedly bounced around local media, although authorities have been loath to single out any country.

In July Thailand deported 109 Uighurs to China, enraging supporters of the minority who allege they face torture and repression back home.

Turkish protesters stormed the Thai consulate in Istanbul and forced it to close.

The Erawan shrine is popular with ethnic Chinese visitors to Bangkok.

The hunt for the perpetrators of the bomb blast has been characterised by confusing and at times contradictory statements from police and junta officials.

But the tempo of the investigation has increased since the weekend, when the first arrest was made.

A foreigner was detained on Saturday at a flat in a Bangkok suburb, allegedly in possession of bomb-making paraphernalia and dozens of fake Turkish passports.

He is in military custody but has not been publicly identified.

Police had previously speculated that the attack was in retaliation for a crackdown on a major people-smuggling network.

But analysts say crime alone was unlikely to be the motivating factor behind a bomb that brought such carnage.

A 26-year-old Thai Muslim woman called Wanna Suansan was named on Monday on another arrest warrant.

Police say she rented a separate flat in the city suburbs where bomb-making equipment was also found.

Thai authorities confirmed Tuesday that Wanna is overseas but refused to say in which country.

Late Monday AFP tracked down her number and a woman answering that name took the phone call, saying she was living in the Turkish city of Kayseri with her husband whose nationality she did not state.

The number was for a Turkish mobile phone.

In her phone interview Wanna denied involvement in the blast, saying she had not visited the flat where the bomb-making equipment was found for around a year.

Instead, she said it had been rented to a friend of her husband.

Police have searched her parents' home in the southern province of Phang Nga but believe she is overseas.