The Thai woman identified Monday by police as a suspect in the Bangkok bombing denied any knowledge of the attack and said she was in Turkey and "shocked" to be linked with the crime.
Thailand's national police spokesman Pol Lt Gen Prawut Thawornsiri holds a tablet displaying a picture of Ms Wanna.
Wanna Suansan, 26, shown in a police photo given to the media on Monday, said she has been in Turkey for the last three months.
She was the first named suspect in the investigation of the Aug 17 bombing, which killed 20 people at the Erawan shrine.
The New York Times reported that Ibrahim Komkham, the headman of the Phang-nga village where Wanna's family lives, said that she had spoken to him by phone, telling him she had left the apartment in June and did not understand why the police thought she was a suspect.
Ms Wanna is willing to come back to Thailand to prove her innocence, he said. He quoted her as saying she would "surrender anywhere, anytime."
On his Twitter account, The New York Times reporter Thomas Fuller said he had confirmed that Ms Wanna had asked police to send her an airplane ticket or the cash to buy one, so that she could return. Mr Fuller said he had learned Ms Wanna claimed she did not have the cash to buy a ticket.
"The warrant is a mistake," he quoted her as saying. "Thailand has made me look like this?"
Police said she had rented an apartment in Min Buri district in northeastern Bangkok, where bomb-making materials were found.
Reporters for the AFP news agency tracked down the number for Wanna and a woman answering that name took the phone call late Monday, saying she was living in the town of Kayseri in Turkey with her husband whose nationality she did not state.
The reporters could not further confirm her identity.
Mrs Wanna, a Thai-speaking Muslim from southern Phang Nga province, said she was horrified when friends in Thailand told her that a photograph from her identity card had been circulated to the Thai public.
"I was very shocked and thought my friend was joking with me," she said.
"I have not been to that apartment for almost one year now... I rented it and then my husband's friend stayed. I don't know how many people stayed there."
"I have been here (Turkey) for around three months," she said, adding Thai police had called her on Monday and asked her "not to worry" and to stay in contact with them.
When AFP called her back later she said she could not speak further since Thai police had warned her not to talk to the media.
Thai police late Monday refused to confirm whether they believed Wanna was in Turkey.
A sketch of a moustachioed male suspect, who police describe as an unidentified foreigner, was also shown during the Thai junta television broadcast.
Police said he too is believed to have rented the flat.
Ms Wanna said she did not recognise the man in the sketch.
The release of Wanna's name and photograph appeared to point to police narrowing down the hunt for the those behind the shrine bomb.
No one has claimed responsibility for the blast and Wanna's denial further clouds an already murky picture of the attack on Thailand.
The man was also found with a stack of fake Turkish passports. That arrest led them to the apartment rented by Wanna.