Counsel for Doan Thi-Huong, Hisham Teh Poh Teik, told the court that she had not slept for the past three nights following the decision by the Malaysian attorney general to drop the charges against Siti.
The other, Indonesian national Siti Aisyah, was freed Monday in a surprise ruling and returned to Indonesia hours later.
Huong's lawyers said CCTV video showing Huong walking up behind Kim and putting her hands over his face should have no bearing on the attorney general's decision, because both women were mounting the same defence and it had already been chose to free Siti Aisyah.
Vietnam urged Malaysia to free Doan Thi Huong, accused of the 2017 VX poison murder of Kim Jong Un's half-brother, a day after a Malaysian court dropped the same charge against an Indonesian woman. "Very obviously, there is discrimination", he said, according to the Associated Press. Malaysia's attorney general ordered the murder case to proceed against the Vietnamese woman accused in the killing of the North Korean leader's estranged half brother.
"It is so unfair. we are calling for help from the most senior people at the trial to consider releasing my daughter, free her as soon as possible", she said. "The AG favored one party to the other".
Vietnam's foreign ministry said it regretted the Malaysian court's decision not to immediately free Huong. The man was dead within 20 minutes, and the women - who said they thought they were taking part in a Japanese game show - were arrested and charged with murder.
Vietnam had increased pressure on Malaysia to release Huong since Aisyah was freed, with the country's foreign minister this week pressing his Malaysian counterpart on the issue and the justice minister writing to the attorney-general. Both women were charged separately but the charge against them is the same: That they had colluded with the four North Korean suspects to murder Kim.
The judge said Huong was not well enough to continue with the trial on Thursday, and adjourned proceedings until April 1.
Some South Korean lawmakers said the North Korean regime had ordered the assassination of Kim Jong Nam, who had been critical of his family's dynastic rule.
Huong's father, Doan Van Thanh, said: "We are very shocked, very sad and we don't understand why it turned out this way".
Lawyers for the women argued that they were pawns in a political assassination with clear links to the North Korean Embassy in Kuala Lumpur, and that the prosecution failed to show the women had any intention to kill. The Guardian reported that Huong looked pale and drawn. She could be seen shaking as she pleaded with Vietnam embassy officials.
Lawyer Ramkarpal Singh speaks to reporters at the Shah Alam High Court January 22, 2019.
The 30-year-old, who could face the death penalty if convicted, sobbed in court when it was announced that her trial would go ahead.
The defence phase of the trial is expected to shift the focus onto the absent North Koreans.
They remain at large despite an Interpol "red notice", equivalent to an global arrest warrant.