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The parents of a 14-year-old boy who fatally shot two people inside a luxury shopping mall in central Bangkok have asked for forgiveness.

A letter, written in Thai by the boy's father and released to the media, states the family is cooperating fully with authorities in the legal process.

The boy faces charges of murder after he opened fire on Tuesday inside the Siam Paragon mall - one of the most-visited shopping centres in Asia.

His motives remain unclear.

In the letter the parents said their son was now in the juvenile observation and protection department as they expressed their "profound sense of regret".

"We offer our deepest apologies to the victims, the families of the deceased and the injured from the recent shooting incident that occurred as the result of our son's actions at the Siam Paragon department store," the statement says.

"This includes the public, tourists, business and store owners and those involved in the incident or nearby who were evacuated and troubled in any way.

"It also includes the medical staff, nurses, police, government officials, whether Thai, Chinese, Myanmar or Lao and all parties affected by this incident. We greatly regret also the damage and impact.

"We are deeply saddened and shocked by this incident and accept responsibility as fully as we can."

Thai authorities charged the teenager on Wednesday with premeditated murder and illegal possession of a firearm. Police said the boy used a modified pistol intended to fire blanks.

His family have not applied for bail.

The two victims who were killed were from China and Myanmar. Five other people - one Lao national, one Chinese and three Thais - were injured.

According to Reuters, police said the boy suffered a psychological breakdown in the run-up to the shooting.

A court turned down a police request to detain the suspect at a mental health facility and ordered him into juvenile detention instead, according to a court document seen by Reuters.