Siti Aisyah, 25, from Indonesia, and Doan Thi Huong, 28, from Vietnam, pleaded not guilty at the Shah Alam High Court on the outskirts of the Malaysian capital.
Police have also named four North Korean suspects in the case and have asked Interpol to help take them into custody.
The trial is expected to last until November 30.
Chaos ensued when photographers were also told they were not allowed to enter the vicinity of the courthouse.
Kim Jong Nam was exiled from North Korea in 2003 and claimed it was for advocating for change in the regime.
Throughout today's proceedings, he is being referred to, however, as "Kim Chol", the name on his passport at the time of his death and the name used by North Korea, which has refused to acknowledge that the man killed was Kim Jong Un's brother.
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During the opening statement on Monday, the prosecution said it would prove that the two women approached Jong Nam at the airport's departure hall and sprayed VX nerve agent on his eyes and face.
According to Malaysian authorities, Kim was at the airport on his way back to see his family in Macau when his face was swabbed with the deadly nerve agent.
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The prosecution stated in its charge sheet the pair's actions showed "intent to kill the victim" by dousing his face and eyes with VX, a nerve agent that is banned by the United Nations.
Mr Kim died in February at Kuala Lumpur's airport in a mysterious case that has gripped the world.
South Korea has accused the North of ordering the hit but Pyongyang denies the allegations.
Dr Nik Mohd Adzrul Ariff Raja Azlan said the 45-year old had very low blood pressure and very low oxygen levels when he arrived at the clinic.
He said he conducted the post-mortem on Jong-nam on Feb 15 after the police handed over the body from the Putrajaya Hospital on Feb 13, 2017. Prosecutors have said they will call multiple expert witnesses to testify to the women's guilt.
Aisyah's lawyer, Gooi Soon Seng, said before the trial began that her defense will be that she didn't know she had poison on her hand when she smeared Kim's face and was instead the victim of an elaborate trick.
Their lawyers argue the women were duped and the true culprits were North Korean agents who told the women what to do. He said Kim was dead on arrival at the hospital.
Deputy public prosecutor Wan Shaharuddin Wan Ladin said it was premature at this stage for the defence to request the names as the prosecution would disclose the names during the trial.