Foreign Minister Pham Binh Minh made the plea in a phone call Tuesday, March 12, 2019, with his counterpart, Saifuddin Abdullah.
The women's lawyers say the real killers are four North Koreans - formally accused of the crime alongside the women - who fled Malaysia shortly after the assassination.
Vietnamese Doan Thi Huong, who is on trial for the killing of Kim Jong-nam, is escorted as she arrives at the Shah Alam High Court on the outskirts of Kuala Lumpur January 22, 2018.
Prosecutors are expected on Thursday to reply to a request by Huong's lawyers for the government to withdraw the murder charge against her as well.
Siti Aisyah and Huong have maintained that they believed they had been hired to take part in a reality TV prank show.
Malaysia's Attorney-General Chambers issued the order last Friday not to prosecute Ms Siti, according to a letter revealed by the Indonesian embassy in Kuala Lumpur yesterday.
Indonesia's government has said its continual high-level lobbying resulted in Aisyah's release. "There was clear evidence and she (Aisyah) confessed", James Chin, a Malaysia specialist at the University of Tasmania, told AFP in a message. I don't know the details.
Aisyah said she hopes Huong is also freed.
Law Minister Liew Vui Keong said Wednesday that the attorney-general has sole discretion in withdrawing the charge against Aisyah.
North Korea has denied any involvement in the plot and argued that the death of North Korean citizen Kim Chol - as Kim Jong-Nam's name appears in the passport he used - was due to a heart attack.
Kim Jong-Nam died on the way to the hospital less than half an hour after receiving the poison that was identified as the VX nerve agent, a colourless and odourless oily liquid classified by the United Nations as a weapon of mass destruction.
Aisyah's swift release had sparked anger in Malaysia, and accusations that the government had caved in to diplomatic pressure.