Commentators in Thailand have criticized numerous missteps in the investigation, including the showing on national television of what appeared to be a suicide vest when the police were revealing evidence seized from an apartment on Saturday. The police later said that the vest had nothing to do with the case.

Image Photos provided by the Thai police and the military government showing what officials say is evidence, including a watch. Credit... Thai Police, via Reuters

The national chief of police had offered a reward of about $84,000 for assistance in finding the perpetrators of the bombing, money that he said had come from his own pocket and that of a friend. On Monday, he announced that the money would be awarded to the police themselves. Officers working on the case deserved the cash, he said.

The authorities issued two warrants on Monday, including one for Wanna Suansan, 27, a woman from a Muslim area in southern Thailand whose family said she had married a Turk and moved to Turkey. Just hours after the release of her name and photograph, Ms. Wanna’s family said she had moved to Turkey months before the shrine attack.

Ibrahim Komkham, the headman of the village in southern Thailand where Ms. 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.