Vietnam's Foreign Minister Pham Binh Binh, in a telephone call to his Malaysian counterpart Datuk Saifuddin Abdullah, asked Malaysia to "ensure a fair trial and free Vietnamese citizen Doan Thi Huong", the government said in a statement.
"There is a law that allows charges to be withdrawn".
Indonesia's government said its continued high-level lobbying had resulted in Aisyah's release and alleged the young migrant worker had no idea she was being "manipulated by North Korean intelligence".
While the court discharged Siti Aisyah from the case, it rejected her lawyer's request for a full acquittal, as it said that the trial had already established a prima facie case and she could be recalled if fresh evidence emerged.
Oh said Vietnam, which hosted North Korean leader Kim Jong Un for an official visit and a summit with President Donald Trump last month, had pushed less hard for Huong.
As the court gave its decision, Ms Siti Aisyah, 26, turned to her Vietnamese co-defendant Doan Thi Huong, 30, in the dock, and the two women, who had been facing the death penalty together, embraced tearfully. They say the real murderers are four North Koreans - formally accused of the crime alongside the women - who fled Malaysia shortly after the assassination.
Watch CCTV camera footage of the attack.
Huong's lawyer, Hisyam Teh Poh Teik, said Huong felt Aisyah's discharge was unfair to her because the judge past year had found sufficient evidence to continue the murder trial against them.
"[I was] shocked at first, I couldn't believe it", Aisyah said of her release.
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Gooi Soon Seng, Siti Aisyah's lawyer, said his client was "a scapegoat".
The two women were accused of smearing the toxic VX nerve agent on Kim's face in an airport terminal in Kuala Lumpur on Feb 13, 2017.
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.
"I still believe that North Korea had something to do with it", Gooi said.
South Korea accuses the North of plotting the murder of Jong Nam, an estranged relative of Kim Jong Un who was once seen as heir apparent to the North Korean leadership.
Vietnam provided legal counsel to Huong, but has refrained from publicly lobbying for her release until Tuesday. Pyongyang denies the accusation.
Then the charges were unexpectedly dropped.
The Straits Times reported that Malaysia made a decision to drop the murder charge against Ms Siti after taking into account the good relations between Malaysia and Indonesia, it was revealed yesterday. "We are making representation to the attorney general for Doan to be taken equally.there must be justice".