Indonesian Siti Aisyah, who accompanied Huong and says she was fooled in the same way, was freed after charges against her were dropped on Monday. Huong's lawyer said the ruling had been marred by discrimination, complaining that the public prosecutor had not "acted fairly and justly" toward his client.
Her lawyer said she had been unable to sleep since the unexpected release of Siti Aisyah, who flew to Jakarta the day she walked free from court.
Huong stood in the dock and responded to the judge's questions on the deferment request, saying she suffered from tension and stress.
"I still believe Huong is innocent", the parking lot attendant said at his home surrounded by rice paddies in Nam Dinh province. The defense phase of the trial was to have begun Monday.
Both women maintain they were tricked into carrying out the attack, which they thought was part of a TV reality show.
Vietnam's Ambassador Le Quy Quynh attended the hearing and said the government was doing all it could to secure Huong's release. He said Vietnam's justice minister had written to the Malaysian attorney-general seeking Huong's release and that Vietnam would keep lobbying Malaysia to free her.
"I don't understand why the other girl was released, but not my daughter", she said.
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Huong was one of two women charged with the February 2017 murder of Kim Jong Nam, an offense punishable by hanging.
Malaysian prosecutors withdrew murder charges against her over the death of the victim.
"God knows that Siti and I did nothing wrong", Huong told reporters in court through an interpreter, according to the Guardian.
Huong is now the only person on trial for the Cold War-style killing, and could face the death penalty if convicted. The government vowed previous year to scrap capital punishment but has indicated this week it would backtrack.
Malaysian officials have never officially accused North Korea and have made it clear they don't want the trial politicized.
Analysts said if North Korea was behind the killing, Kim Jong Un may have seen his older half-brother as a potential leadership threat - even though their father, former North Korean leader Kim Jong Il, had long discounted Kim Jong Nam as a possible successor. He had been living overseas for years but could have been seen as a threat to Kim Jong Un's rule.